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Фундаментальные вопросы по ML/DL, часть 1: Вопрос → Краткий ответ → Разбор → Пример кода. Линейки. Байес. Регуляризация

У каждого наступает момент, когда нужно быстро освежить в памяти огромный пласт информации по всему ML. Причины разные - подготовка к собеседованию, начало преподавания или просто найти вдохновение.

Времени мало, объема много, цели амбициозные - нужно научиться легко и быстро объяснять, но так же не лишая полноты!

Обращу внимание, самый действенный способ разобраться и запомнить - это своими руками поисследовать задачу! Это самое важное, оно происходит в секции с кодом.

Будет здорово получить ваши задачи и в следующих выпусках разобрать!

Я считаю самый полный и простой способ заполнить все пробелы - это взять хороший экзамен и ответить на все вопросы - понятно и быстро. А что запомнилось решить задачку. Приступим!

Сначала попробуйте сами быстро ответить, а потом после просмотра! Стало быстрее-понятнее объяснять?

Для более полного погружения в конце приложу важные ресурсы. Делитесь своими!

📚 Глава 1: Модели, метрики и формула Байеса

0. Задача обучения с учителем. Регрессия, Классификация

📌 Краткий ответ

Обучение с учителем — это постановка задачи, при которой каждый объект обучающей выборки снабжён целевым значением , и модель обучается приближать отображение $f(x) \approx y$ .
Регрессия: если $y \in \mathbb{R}$ (например, цена, температура).
Классификация: если $y \in \{1, \dots, K\}$ , то есть класс или категория (например, диагноз, категория изображения).

🔬 Подробный разбор

Общая постановка задачи

В обучении с учителем задана обучающая выборка из пар

$(x_i, y_i), \quad i = 1, \dots, n,$

где $x_i \in \mathbb{R}^d$ — вектор признаков, y_i — целевая переменная. Требуется построить алгоритм f(x) , минимизирующий ошибку предсказания.

Регрессия

Если $y_i \in \mathbb{R}$ или $\mathbb{R}^k$ , задача называется регрессией.
Модель должна предсказывать численное значение. Типичные функции потерь:

Mean Squared Error (MSE)
Mean Absolute Error (MAE)

Примеры:

Прогнозирование цены недвижимости
Оценка спроса на товар

Классификация

Если $y_i \in \{1, \dots, K\}$ — задача классификации.
В простейшем случае — бинарная классификация (например, "да/нет").
При

K > 2 — многоклассовая. Также существует multi-label классификация, когда одному объекту соответствуют несколько меток.

Модель выдает либо вероятности по классам (soft), либо сразу метку (hard). Часто оптимизируют logloss или используют surrogate-функции.

Примеры:

Распознавание рукописных цифр (0–9)
Классификация e-mail как "спам / не спам"

💻 Отрисовываем предсказания линейной и логистической регресии

Заглянем чуть дальше и покажем, пример решения задачи регресии (линейной регрессией) и классификации (логистической регрессией)

from sklearn.linear_model import LinearRegression, LogisticRegression
from sklearn.datasets import make_regression, make_classification

# --- Регрессия ---
X_reg, y_reg = make_regression(n_samples=100, n_features=2, noise=0.1, random_state=43) # [100, 2], [100]
reg = LinearRegression().fit(X_reg, y_reg)

# --- Классификация ---
X_clf, y_clf = make_classification(n_samples=100, n_features=2, n_classes=2, n_redundant=0, random_state=43) # [100, 2], [100]
clf = LogisticRegression().fit(X_clf, y_clf)



# --- Отрисовка ---
import matplotlib.pyplot as plt
import numpy as np

# Создаем фигуру с двумя подграфиками
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 5))

# --- Регрессия ---
# Создаем сетку точек для линии регрессии
x_grid = np.linspace(X_reg[:, 0].min(), X_reg[:, 0].max(), 100).reshape(-1, 1)
# Добавляем второй признак (среднее значение) # отрисовать только 1 признак можем => по второму усредним! 
# так делать очень плохо! но для игрушечного примера - ок!
x_grid_full = np.column_stack([x_grid, np.full_like(x_grid, X_reg[:, 1].mean())])
y_pred = reg.predict(x_grid_full)

# Визуализация регрессии
ax1.scatter(X_reg[:, 0], y_reg, alpha=0.5, label='Данные')
ax1.plot(x_grid, y_pred, 'r-', label='Линия регрессии')
ax1.set_title('Регрессия')
ax1.set_xlabel('Признак 1')
ax1.set_ylabel('Целевая переменная')
ax1.legend()

# --- Классификация ---
# Создаем сетку точек для границы принятия решений
x_min, x_max = X_clf[:, 0].min() - 0.5, X_clf[:, 0].max() + 0.5
y_min, y_max = X_clf[:, 1].min() - 0.5, X_clf[:, 1].max() + 0.5
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02),
                     np.arange(y_min, y_max, 0.02))

# Предсказываем классы для всех точек сетки
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

# Визуализация классификации
ax2.contourf(xx, yy, Z, alpha=0.3, cmap='viridis')
ax2.contour(xx, yy, Z, [0.5], colors='red', linewidths=2)

scatter = ax2.scatter(X_clf[:, 0], X_clf[:, 1], c=y_clf, cmap='viridis', alpha=0.5)
ax2.set_title('Классификация')
ax2.set_xlabel('Признак 1')
ax2.set_ylabel('Признак 2')
ax2.legend(*scatter.legend_elements(), title="Классы")

plt.tight_layout()
plt.show()

1. Метрики классификации: accuracy, balanced accuracy, precision, recall, f1-score, ROC-AUC, расширения для многоклассовой классификации

📌 Краткий ответ

Для задачи бинарной классификации ( $y \in {0, 1}$ ) можно построить матрицу ошибок и по ним посчитать метрики:

Метрика	Формула	Смысл
Accuracy	`Accuracy = (TP + TN) / (TP + TN + FP + FN)`	Общая доля правильных предсказаний
Balanced Accuracy	`0.5 * (TPR + TNR) = 0.5 * (TP / (TP + FN) + TN / (TN + FP))`	Усреднённая точность по классам при дисбалансе
Precision	`TP / (TP + FP)`	Доля верных положительных предсказаний
Recall	`TP / (TP + FN)`	Доля найденных положительных среди всех реальных
F1(b)-score	`2 * P * R / (P + R) = 2 / (1/P + 1/R) = [b=1] = (b^2 + 1) / (b^2 r^-1 + r^-1)`	Баланс между precision и recall
AUC	Доля правильно упорядоченных пар среди (Negative, Positive)	Площадь под ROC-кривой (TPR (y) vs FPR (x) при разных порогах)

Легче запомнить, как TPR = recall позитивного класса, а FPR = 1 - recall негативного класса !

Как по мне самое простое и полезное переформулировка - это доля правильно упорядоченных пар среди (Negative, Positive)

Самый плохой случай - AUC=0.5 иначе можно реверснуть!
Лучшая метрика AUC=1

Для многоклассовой классификации - считаем для каждого класса one-vs-rest матрицу ошибок. Далее либо микро-усредняем (суммируем компоненты и считаем метрку) или макро-усреднение (по классам считаем и усредняем)

🔬 Подробный разбор

Очень подробно расписано здесь!

Обратите внимание так же на:

Recall@k, Precision@k
Average Precision

В следующих статьях будем отвечать на вопросы из практике - там и разгуляемся (иначе можно закапаться)!

💻 Визуализируем AUC ROC


from sklearn.datasets import make_classification
from sklearn.linear_model import LogisticRegression
from sklearn.dummy import DummyClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import roc_curve, roc_auc_score
import matplotlib.pyplot as plt

# --- 1. Синтетические, "грязные" данные ---
X, y = make_classification(
    n_samples=1000,
    n_features=20,
    n_informative=5,
    n_redundant=4,
    n_classes=2,
    weights=[0.75, 0.25],  # дисбаланс классов
    flip_y=0.1,            # 10% меток шумные
    class_sep=0.8,         # классы частично пересекаются
    random_state=42
)

# --- 2. Деление на train/test ---
X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size=0.3, random_state=42)

# --- 3. Логистическая регрессия ---
model = LogisticRegression(max_iter=1000).fit(X_tr, y_tr)
y_prob = model.predict_proba(X_te)[:, 1]
fpr_model, tpr_model, _ = roc_curve(y_te, y_prob)
auc_model = roc_auc_score(y_te, y_prob)

# --- 4. Dummy-классификатор (стратегия stratified) ---
dummy = DummyClassifier(strategy='stratified', random_state=42).fit(X_tr, y_tr)
y_dummy_prob = dummy.predict_proba(X_te)[:, 1]
fpr_dummy, tpr_dummy, _ = roc_curve(y_te, y_dummy_prob)
auc_dummy = roc_auc_score(y_te, y_dummy_prob)

# --- 5. Визуализация ROC-кривых ---
plt.figure(figsize=(8, 6))
plt.plot(fpr_model, tpr_model, label=f"Logistic Regression (AUC = {auc_model:.2f})")
plt.plot(fpr_dummy, tpr_dummy, linestyle='--', label=f"Dummy Stratified (AUC = {auc_dummy:.2f})")
plt.plot([0, 1], [0, 1], 'k:', label="Random Guess (AUC = 0.50)")

plt.xlabel("False Positive Rate (FPR)")
plt.ylabel("True Positive Rate (TPR)")
plt.title("ROC-кривая: логистическая регрессия vs случайный классификатор")
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

2. Метрики регрессии: MSE, MAE, R²

📌 Краткий ответ

Метрика	Формула	Смысл
MSE	`mean((y_true - y_pred) ** 2)`	Среднеквадратичная ошибка. Наказывает большие ошибки сильнее.
MAE	`mean(abs(y_true - y_pred))`	Средняя абсолютная ошибка. Интерпретируется в исходных единицах.
R² score	`1 - MSE_model / MSE_const`	На сколько лучше константного предсказания(=среднее при минимизации MSE) . От 0 до 1 (может быть < 0 при плохой модели).

🔬 Подробный разбор

MSE (Mean Squared Error)
Наиболее распространённая функция потерь. Ошибки возводятся в квадрат, что делает метрику чувствительной к выбросам.
MSE = mean((y - ŷ) ** 2)

MAE (Mean Absolute Error)
Абсолютное отклонение между предсказаниями и истиной. Менее чувствительна к выбросам(=робастнее), хорошо интерпретируется (в тех же единицах, что и целевая переменная).
MAE = mean(|y - ŷ|)

Huber Loss — гибрид между MSE и MAE: локально квадратичный штраф, дальше линейный.

R² (коэффициент детерминации)
Показывает, какую часть дисперсии целевой переменной объясняет модель.
R² = 1 - (MSE_model / MSE_const)
Где MSE_const — ошибка наивной модели, предсказывающей среднее.

💻 Сравниваем функции ошибок

from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from sklearn.datasets import make_regression
from sklearn.linear_model import LinearRegression, HuberRegressor
from sklearn.model_selection import train_test_split

# Данные
X, y = make_regression(n_samples=500, noise=15, random_state=42)
X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size=0.3, random_state=42)

# --- Линейная регрессия ---
model_lr = LinearRegression().fit(X_tr, y_tr)
y_pred_lr = model_lr.predict(X_te)

print("=== Linear Regression ===")
print("MSE:", mean_squared_error(y_te, y_pred_lr))
print("MAE:", mean_absolute_error(y_te, y_pred_lr))
print("R²:", r2_score(y_te, y_pred_lr))

# --- Huber-регрессия ---
model_huber = HuberRegressor().fit(X_tr, y_tr)
y_pred_huber = model_huber.predict(X_te)

print("\n=== Huber Regressor ===")
print("MSE:", mean_squared_error(y_te, y_pred_huber))
print("MAE:", mean_absolute_error(y_te, y_pred_huber))
print("R²:", r2_score(y_te, y_pred_huber))

=== Linear Regression ===
MSE: 334.45719591398216
MAE: 14.30958669001259
R²: 0.988668164971938

=== Huber Regressor ===
MSE: 367.2515287731075
MAE: 15.169297076822216
R²: 0.9875570512797974

Эти метрики - они могут быть как лосс функциями, так и бизнесс метриками! Какой лосс минимизировать, нужно понять какая целевая бизнес метрика!

import numpy as np
import matplotlib.pyplot as plt

# Ошибки (residuals)
errors = np.linspace(-2, 2, 400)

# MSE: квадратичные потери
mse_loss = errors ** 2

# MAE: абсолютные потери
mae_loss = np.abs(errors)

# Huber loss
delta = 1.0
huber_loss = np.where(
    np.abs(errors) <= delta,
    0.5 * errors ** 2,
    delta * (np.abs(errors) - 0.5 * delta)
)

# Визуализация
plt.figure(figsize=(8, 6))
plt.plot(errors, mse_loss, label='MSE Loss', color='red')
plt.plot(errors, mae_loss, label='MAE Loss', color='blue')
plt.plot(errors, huber_loss, label='Huber Loss (δ = 1.0)', color='green')
plt.xlabel("Ошибка (residual)")
plt.ylabel("Значение функции потерь")
plt.title("Сравнение MSE, MAE и Huber Loss")
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

3. Оценка максимального правдоподобия (MLE), связь с регрессией и классификацией

📌 Краткий ответ

MLE (Maximum Likelihood Estimation) — метод оценки параметров, при котором максимизируется вероятность наблюдаемых данных.

Целевая переменная (и параметры модели) рассматриваются как слуайные величины.

Фиксируем класс моделей (например линейные) и ищем максимально правдоподобную модель среди них (=> нужно определить вероятность наблюдаемого семпла и при выводк воспользоваться независимостью семплов)!

В линейной регрессии (при нормальном шуме) MLE ⇔ минимизация MSE
В логистической регрессии MLE ⇔ минимизация логлосса
Регуляризация вносит априорные предположения (MAP) на веса. При нормальном, получаем регуляризацию, при лаплассе .

🔬 Формальные выводы

Детальнее можно узнать в конце тетрадке.

✍ MLE и линейная регрессия

Предполагаем, что целевая переменная yᵢ имеет нормальное распределение с центром в xᵢᵀw и дисперсией σ²:

$y_i \sim \mathcal{N}(x_i^\top w, \sigma^2)$

Тогда правдоподобие всей выборки:

$p(y | X, \theta) = \prod_i \mathcal{N}(y_i | x_i^\top w, \sigma^2)$

Берём логарифм:

$\log p(y | X, \theta) = \sum_i \log \left( \frac{1}{\sqrt{2\pi} \sigma} \exp\left( -\frac{(y_i - x_i^\top w)^2}{2\sigma^2} \right) \right)$

Раскрываем сумму:

$= \sum_i \left( -\frac{1}{2} \log(2\pi) - \log \sigma - \frac{(y_i - x_i^\top w)^2}{2\sigma^2} \right)$

→ максимизация логарифма правдоподобия эквивалентна минимизации:

$\sum_i (y_i - x_i^\top w)^2$

✅ Вывод:

Метод максимального правдоподобия (MLE) для линейной регрессии приводит к функции потерь MSE — среднеквадратичной ошибке.

Регуляризация (например, Ridge(=)) возникает при добавлении априорного распределения на веса — это уже MAP, не MLE.

✍ MLE и логистическая регрессия

В бинарной классификации целевая переменная yᵢ ∈ {0, 1} - для отклонения используем распределние Бернули.

Предполагаем:

$P(y_i = 1 | x_i, w) = \sigma(x_i^\top w) = \frac{1}{1 + e^{-x_i^\top w}}$

Правдоподобие всей выборки:

$L(w) = \prod_i \left[ \sigma(x_i^\top w) \right]^{y_i} \cdot \left[ 1 - \sigma(x_i^\top w) \right]^{1 - y_i}$

Логарифм правдоподобия:

$\log L(w) = \sum_i \left[ y_i \log \sigma(x_i^\top w) + (1 - y_i) \log (1 - \sigma(x_i^\top w)) \right]$

✅ Вывод:

Максимизация логарифма правдоподобия ⇔ минимизация log-loss (логистической функции потерь)

✍ Что меняется с регуляризацией: MAP (Maximum A Posteriori)

Добавим априорное распределение на параметры:

L2-регуляризация ⇔ априорное w ∼ 𝒩(0, λ⁻¹I)
L1-регуляризация ⇔ априорное w ∼ Laplace(0, b)

MAP-оценка:

$\log P(w | X, y) ∝ \log L(w) + \log P(w)$

→ Это и есть MLE + регуляризация:

MLE ⇔ логлосс
MAP ⇔ логлосс + регуляризация

💻 Баесовский вывод двух нормальных распределений

Задача

Пусть параметр неизвестен и:

Prior: $w \sim \mathcal{N}(\mu_0, \sigma_0^2)$
Likelihood: $y \sim \mathcal{N}(\mu_1, \sigma_1^2)$ — наблюдение, связанное с

Найти posterior $P(w \mid y)$

📐 Шаг 1: формула Байеса

По определению:

$P(w | y) \propto P(y | w) \cdot P(w)$

Логарифмируем обе части:

$\log P(w | y) = \log P(y | w) + \log P(w) + \text{const}$

🧮 Шаг 2: подставляем нормальные распределения

Prior:

$\log P(w) = -\frac{1}{2\sigma_0^2} (w - \mu_0)^2 + \text{const}$

Likelihood (в терминах , фиксируя $y = \mu_1$ ):

$\log P(y | w) = -\frac{1}{2\sigma_1^2} (w - \mu_1)^2 + \text{const}$

📉 Шаг 3: складываем логарифмы

$\log P(w | y) = -\frac{1}{2\sigma_0^2} (w - \mu_0)^2 - \frac{1}{2\sigma_1^2} (w - \mu_1)^2 + \text{const}$

Это — квадратичная функция по , то есть логарифм нормального распределения. Следовательно, сам posterior — тоже нормальный:

$P(w | y) = \mathcal{N}(\mu_{\text{post}}, \sigma_{\text{post}}^2)$

✅ Вывод: параметры апостериорного распределения

$\sigma_{\text{post}}^2 = \left( \frac{1}{\sigma_0^2} + \frac{1}{\sigma_1^2} \right)^{-1}$ $\mu_{\text{post}} = \sigma_{\text{post}}^2 \left( \frac{\mu_0}{\sigma_0^2} + \frac{\mu_1}{\sigma_1^2} \right)$

Отрисуем!

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm

# Ось параметра w
w = np.linspace(-5, 5, 500)

# Заданные параметры
mu0, sigma0 = 0, 1     # prior: N(0, 1)
mu1, sigma1 = 2, 1     # likelihood: N(2, 1)

# Распределения
prior = norm.pdf(w, loc=mu0, scale=sigma0)
likelihood = norm.pdf(w, loc=mu1, scale=sigma1)

# Постериорное распределение — аналитически
sigma_post_sq = 1 / (1/sigma0**2 + 1/sigma1**2)
mu_post = sigma_post_sq * (mu0/sigma0**2 + mu1/sigma1**2)
posterior = norm.pdf(w, loc=mu_post, scale=np.sqrt(sigma_post_sq))

# Визуализация
plt.figure(figsize=(10, 6))
plt.plot(w, prior, label=f"Prior N({mu0}, {sigma0**2})", color='green')
plt.plot(w, likelihood, label=f"Likelihood N({mu1}, {sigma1**2})", color='blue')
plt.plot(w, posterior, label=f"Posterior N({mu_post:.2f}, {sigma_post_sq:.2f})", color='red')

plt.axvline(mu0, color='green', linestyle=':')
plt.axvline(mu1, color='blue', linestyle=':')
plt.axvline(mu_post, color='red', linestyle='--', label=f"MAP = {mu_post:.2f}")

plt.title("Байесовский вывод: Posterior = Prior × Likelihood")
plt.xlabel("w")
plt.ylabel("Плотность")
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

На самом деле, даже для двух многмерных нормальных распределений с разными дисперсиями - верно следующее, их апостериальное распределение тоже нормальное!

4. Наивный байесовский классификатор

📌 Краткий ответ

Наивный байесовский классификатор предполагает, что все признаки условно независимы при фиксированном классе:

$P(y | x_1, ..., x_d) ∝ P(y) \cdot \prod_{i=1}^d P(x_i | y)$

Обучение: оцениваем P(y) и P(xᵢ | y) по каждому признаку.
Работает быстро, устойчив к малым выборкам, можно задавать разные распределения.

🔬 Подробный разбор

В логарифмической форме:

$\log P(y | x) ∝ \log P(y) + \sum_i \log P(x_i | y)$

Можно использовать:

Гауссовское распределение — GaussianNB
Ядерную оценку плотности (KDE) — сглаженные вероятности
Экспоненциальное, Лапласовское и др.

Преимущество подхода: можно подставлять разные распределения под разные признаки.

💻 Наивный Баейс на практике с разными распределениями признаков (KDE)

Полная тетрадка тут.

Для простоты будем работать не со всеми 4 признаками, а с двумя!

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.neighbors import KernelDensity
from sklearn.metrics import accuracy_score
from sklearn.naive_bayes import GaussianNB
from scipy.special import logsumexp

# --- 1. Загрузка и подготовка данных
iris = load_iris()
X = iris.data[:, [2, 3]]  # два признака: длина и ширина лепестка
y = iris.target
feature_names = np.array(iris.feature_names)[[2, 3]]
class_names = iris.target_names

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

# --- 2. Обёртка KDE
class KDEWrapper:
    def __init__(self, data):
        self.kde = KernelDensity(kernel='gaussian', bandwidth=0.2).fit(data[:, None])

    def logpdf(self, x):
        return self.kde.score_samples(x[:, None])
    

#  --- 3. NaiveBayes из тетрадки
class NaiveBayes:
    def fit(self, X, y, sample_weight=None, distributions=None):
        self.unique_labels = np.unique(y)
        if distributions is None:
            distributions = [KDEWrapper] * X.shape[1]
        assert len(distributions) == X.shape[1]
        self.conditional_feature_distributions = {}
        for label in self.unique_labels:
            dists = []
            for i in range(X.shape[1]):
                dists.append(distributions[i](X[y == label, i]))
            self.conditional_feature_distributions[label] = dists
        self.prior_label_distibution = {l: np.mean(y == l) for l in self.unique_labels}

    def predict_log_proba(self, X):
        log_proba = np.zeros((X.shape[0], len(self.unique_labels)))
        for i, label in enumerate(self.unique_labels):
            for j in range(X.shape[1]):
                log_proba[:, i] += self.conditional_feature_distributions[label][j].logpdf(X[:, j])
            log_proba[:, i] += np.log(self.prior_label_distibution[label])
        log_proba -= logsumexp(log_proba, axis=1)[:, None]
        return log_proba

    def predict(self, X):
        return self.unique_labels[np.argmax(self.predict_log_proba(X), axis=1)]

# --- 4. Обучение моделей
model_kde = NaiveBayes()
model_kde.fit(X_train, y_train, distributions=[KDEWrapper, KDEWrapper])
y_pred_kde = model_kde.predict(X_test)

model_gnb = GaussianNB()
model_gnb.fit(X_train, y_train)
y_pred_gnb = model_gnb.predict(X_test)

print("KDE NB Accuracy:", accuracy_score(y_test, y_pred_kde))
print("GaussianNB Accuracy:", accuracy_score(y_test, y_pred_gnb))

# KDE NB Accuracy: 1.0
# GaussianNB Accuracy: 1.0

# --- 5. Визуализация KDE-плотностей
def plot_kde_and_gaussian_densities(X_data, y_data):
    fig, axes = plt.subplots(1, 2, figsize=(12, 4))
    
    # Обучим GaussianNB — он сам оценит параметры
    gnb = GaussianNB()
    gnb.fit(X_data, y_data)

    for i in range(X_data.shape[1]):
        ax = axes[i]
        for label in np.unique(y_data):
            x_vals = X_data[y_data == label, i]
            grid = np.linspace(x_vals.min() * 0.9, x_vals.max() * 1.1, 500)

            # --- KDE
            kde = KernelDensity(kernel='gaussian', bandwidth=0.2).fit(x_vals[:, None])
            ax.plot(grid, np.exp(kde.score_samples(grid[:, None])), label=f'{class_names[label]} (KDE)', linestyle='-')

            # --- Gauss via GaussianNB
            mu = gnb.theta_[label, i]
            sigma = np.sqrt(gnb.var_[label, i])
            ax.plot(grid, norm.pdf(grid, mu, sigma), label=f'{class_names[label]} (Gauss)', linestyle='--')


        ax.set_title(f'Плотности для {feature_names[i]}')
        ax.set_xlabel('Значение признака')
        ax.set_ylabel('Плотность')
        ax.legend()
        ax.grid()

    plt.tight_layout()
    plt.show()

# --- 6. Визуализация границ решений
def plot_decision_boundary(X_data, y_data, model, title):
    x_min, x_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5
    y_min, y_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5
    xx, yy = np.meshgrid(np.linspace(x_min, x_max, 300),
                         np.linspace(y_min, y_max, 300))
    grid = np.c_[xx.ravel(), yy.ravel()]
    Z = model.predict(grid).reshape(xx.shape)

    plt.figure(figsize=(8, 6))
    plt.contourf(xx, yy, Z, alpha=0.3, cmap='Accent')
    plt.contour(xx, yy, Z, levels=np.arange(0, 4), colors='k', linewidths=0.5)
    for label in np.unique(y_train):
        plt.scatter(X_data[y_data == label, 0], X_data[y_data == label, 1],label=class_names[label], s=40)
    plt.xlabel(feature_names[0])
    plt.ylabel(feature_names[1])
    plt.title(title)
    plt.legend()
    plt.grid(True)
    plt.tight_layout()
    plt.show()

# train
plot_kde_and_gaussian_densities(X_train, y_train)
plot_decision_boundary(X_train, y_train, model_kde, "Наивный Байес с KDE")
plot_decision_boundary(X_train, y_train, model_gnb, "GaussianNB (Гауссовский Наивный Байес)")
# test
plot_kde_and_gaussian_densities(X_test, y_test)
plot_decision_boundary(X_test, y_test, model_kde, "Наивный Байес с KDE")
plot_decision_boundary(X_test, y_test, model_gnb, "GaussianNB (Гауссовский Наивный Байес)")

5. Метод ближайших соседей

📌 Краткий ответ

Метод k ближайших соседей (k-NN) — это ленивый классификатор, который:

не обучается явно
при предсказании ищет k ближайших объектов в обучающей выборке
голосует за класс большинства (или усредняет — в регрессии).

Работает по метрике (например, евклидовой), чувствителен к масштабу и шуму.

🔬 Подробный разбор

При классификации:

ŷ(x) = argmax_c ∑ I(yᵢ = c) для xᵢ ∈ N_k(x)

Плюсы:

не требует обучения,
хорошо работает на небольших данных.

Минусы:

не масштабируется (хранит всё),
чувствителен к размерности и шуму,
требует нормализации признаков.

Гиперпараметры:

k — число соседей (подбирается на валидации),
metric — метрика расстояния (евклидово, косинусное и т.д.)

💻 Пишем свой KNN и сравниваемся с библиотечным на MNIST

import numpy as np
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import accuracy_score
from scipy.stats import mode

# --- 1. Загружаем данные
digits = load_digits()
X = digits.data
y = digits.target

# Масштабирование
X = StandardScaler().fit_transform(X)

# Разделение
X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size=0.3, random_state=42)

# --- 2. Своя реализация k-NN (евклидовая метрика)
class MyKNN:
    def __init__(self, n_neighbors=5):
        self.k = n_neighbors

    def fit(self, X, y):
        self.X_train = X
        self.y_train = y

    def predict(self, X):
        predictions = []
        for x in X:
            dists = np.linalg.norm(self.X_train - x, axis=1)
            nearest = np.argsort(dists)[:self.k]
            labels = self.y_train[nearest]
            pred = mode(labels, keepdims=False).mode 
            predictions.append(pred)
        return np.array(predictions)

# --- 3. Обучение и сравнение
# sklearn
sk_knn = KNeighborsClassifier(n_neighbors=5)
sk_knn.fit(X_tr, y_tr)
y_pred_sk = sk_knn.predict(X_te)
acc_sk = accuracy_score(y_te, y_pred_sk)

# наш
my_knn = MyKNN(n_neighbors=5)
my_knn.fit(X_tr, y_tr)
y_pred_my = my_knn.predict(X_te)
acc_my = accuracy_score(y_te, y_pred_my)

assert np.isclose(acc_sk, acc_my, rtol=1e-6), 'Точности не совпдают!'
print(f"{acc_sk=} {acc_my=}")
# acc_sk=0.9777777777777777 acc_my=0.9777777777777777

📊 Глава 2: Почему линейная модель — это не просто прямая

6. Линейная регрессия. Формулировка задачи для случая функции потерь MSE. Аналитическое решение. Теорема Гаусса-Маркова. Градиентный подход в линейной регрессии.

📌 Краткий ответ

Линейная регрессия минимизирует MSE:

$L(w) = \|Xw - y\|^2$

Аналитически: $\hat{w} = (X^\top X)^{-1} X^\top y$
Теорема Гаусса-Маркова: это наилучшая линейная несмещённая оценка при стандартных предположениях (BLUE)
При больших данных: используется градиентный спуск

🔬 Подробный разбор

📌 Постановка задачи

У нас есть:

$X \in \mathbb{R}^{n \times d}$ — матрица признаков;
$y \in \mathbb{R}^n$ — целевая переменная;
$w \in \mathbb{R}^d$ — веса модели.

Цель: минимизировать среднеквадратичную ошибку:

$L(w) = \|Xw - y\|^2 = (Xw - y)^\top (Xw - y)$

📌 Вывод аналитического решения

Выпишем градиент по :

$\nabla_w L(w) = 2 X^\top (Xw - y)$

Приравниваем к нулю:

$X^\top (Xw - y) = 0$

Раскрываем скобки:

$X^\top X w = X^\top y$

Предполагая, что $X^\top X$ обратима:

$\hat{w} = (X^\top X)^{-1} X^\top y$

📌 Теорема Гаусса-Маркова (формулировка)

Если:

модель линейна по параметрам: $y = Xw + \varepsilon$ ;
ошибки $\varepsilon$ имеют нулевое среднее;
одинаковую дисперсию $\text{Var}(\varepsilon) = \sigma^2 I$ ;
некоррелированы между собой;

→ тогда $\hat{w}$ (из нормального уравнения) — наилучшая линейная несмещённая оценка (BLUE).

Термин BLUE (Best Linear Unbiased Estimator) — это сокращение:

Linear (линейная):
Оценка $\hat{w}$ — это линейная функция от :
$\hat{w} = A y$
где $A = (X^\top X)^{-1} X^\top$
Unbiased (несмещённая):
Среднее значение оценки совпадает с истинным параметром:
$\mathbb{E}[\hat{w}] = w$
Best (наилучшая):
Из всех линейных и несмещённых оценок, $\hat{w}$ имеет наименьшую дисперсию:
$\text{Var}(\hat{w}) \text{ минимальна среди всех линейных несмещённых оценок}$

💻 Аналитическое и градиентное решение поиска весов линейной модели + график

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_regression
from sklearn.metrics import mean_squared_error

# --- Данные
X_raw, y = make_regression(n_samples=300, n_features=1, noise=15, random_state=42)
X = np.hstack([X_raw, np.ones((X_raw.shape[0], 1))])  # добавим bias

# --- Аналитическое решение
w_analytic = np.linalg.inv(X.T @ X) @ X.T @ y
y_pred_analytic = X @ w_analytic

# --- Градиентный спуск
w = np.zeros(X.shape[1])
lr = 0.01
losses = []

for _ in range(1000):
    grad = 2 * X.T @ (X @ w - y) / len(y)
    w -= lr * grad
    losses.append(mean_squared_error(y, X @ w))

y_pred_gd = X @ w

# --- Сравнение
print("MSE (аналитика):", mean_squared_error(y, y_pred_analytic))
print("MSE (градиент):", mean_squared_error(y, y_pred_gd))

# --- Визуализация
plt.figure(figsize=(10, 5))

# 1. Предсказания
plt.subplot(1, 2, 1)
plt.scatter(X_raw, y, s=20, alpha=0.6, label='Данные')
plt.plot(X_raw, y_pred_analytic, label='Аналитическое решение', color='green')
plt.plot(X_raw, y_pred_gd, label='Градиентный спуск', color='red', linestyle='--')
plt.title("Сравнение решений")
plt.xlabel("X")
plt.ylabel("y")
plt.legend()
plt.grid()

# 2. Потери во времени
plt.subplot(1, 2, 2)
plt.plot(losses, label="MSE (градиент)")
plt.title("Сходимость градиента")
plt.xlabel("Итерации")
plt.ylabel("MSE")
plt.grid()
plt.tight_layout()
plt.show()
# MSE (аналитика): 230.84267462302407
# MSE (градиент): 230.84267462302407

7. Регуляризация в линейных моделях: L_1 ,L_2 их свойства. Вероятностная интерпретация.

📌 Краткий ответ

Регуляризация — это добавка к функции потерь, которая ограничивает рост весов и борется с переобучением.

L2-регуляризация (Ridge):
$\text{Loss}(w) = \text{MSE}(w) + \lambda \|w\|_2^2$
L1-регуляризация (Lasso):
$\text{Loss}(w) = \text{MSE}(w) + \lambda \|w\|_1$
L2 сглаживает и уменьшает веса
L1 приводит к разреженным решениям (обнуляет ненужные признаки)

🔬 Подробный разбор

L_2 - Ridge, L_1 - Lasso, Elastic Net - комбинация.

📌 Вероятностная интерпретация

Добавление регуляризатора эквивалентно введению априорного распределения на параметры (подробнее в 3 вопросе о MLE):

L2 = Gaussian prior:
$P(w) \sim \mathcal{N}(0, \sigma^2 I)\Rightarrow \text{MAP} \propto \log L(w) - \lambda \|w\|_2^2$
L1 = Laplace prior:
$P(w) \sim \text{Laplace}(0, b)\Rightarrow \text{MAP} \propto \log L(w) - \lambda \|w\|_1$

→ То есть регуляризация = байесовская MAP-оценка, если мы знаем prior на веса.

Почему при зануляются веса?

Очень популярный и важный вопрос! Изобразим уровни потерь по отдельности двух частей лосса!

Предпложим противное. Пусть t^* опитимум пересечения и он не на осях координат. Из-за выпуклости двух фигур, найдется пересечения внутри, а по нему можно уже подняться вверх, сохранив ошибку по L_1 и уменьшить MSE ! Второй заумный аргумент .

Упрощение 2-аргумента: две фигуры выпуклые и имеют единственную касательную (помимо L_1 в точках на осях!), тогда в точке касания можно провести разделяющую прямую!

А это значит, что оси у элипса у MSE параллельны фиксированному направлению, а вероятность таких направлений (на одну размерность меньше=) равна нулю!

💻 Сравниваем веса моделей с L1 и L2

Обучим две модельки с разными регулизаторами на данных с 8 из 10 шумных признаками. В идеали избавиться(иметь вес ноль) от всех неинформативных признаков!

# Генерируем данные: 2 полезных признака + 8 шумовых

from sklearn.linear_model import Ridge, Lasso
from sklearn.metrics import mean_squared_error
import numpy as np
import matplotlib.pyplot as plt

# --- Параметры
n_samples = 100
n_features = 10
n_informative = 2  # только два признака "полезные"

# --- Генерация данных
np.random.seed(42)
X = np.random.randn(n_samples, n_features)
true_coefs = np.zeros(n_features)
true_coefs[:n_informative] = [3, -2]  # только первые 2 признака значимы

# Целевая переменная с шумом
y = X @ true_coefs + np.random.normal(0, 1.0, size=n_samples)

# --- Обучение моделей
ridge = Ridge(alpha=1.0)
lasso = Lasso(alpha=0.1)

ridge.fit(X, y)
lasso.fit(X, y)

# --- Сравнение весов
x_idx = np.arange(n_features)
plt.figure(figsize=(10, 4))
plt.stem(x_idx, true_coefs, linefmt="gray", markerfmt="go", basefmt=" ", label="True")
plt.stem(x_idx, ridge.coef_, linefmt="b-", markerfmt="bo", basefmt=" ", label="Ridge")
plt.stem(x_idx, lasso.coef_, linefmt="r-", markerfmt="ro", basefmt=" ", label="Lasso")
plt.xticks(ticks=x_idx)
plt.title("L1 vs L2: 2 информативных признака, остальные шум")
plt.xlabel("Индекс признака")
plt.ylabel("Вес")
plt.legend()
plt.tight_layout()
plt.show()

# --- Подсчёт зануленных весов
ridge_zeros = np.sum(np.abs(ridge.coef_) < 1e-4)
lasso_zeros = np.sum(np.abs(lasso.coef_) < 1e-4)
print(f"{ridge_zeros=}, f{lasso_zeros=}")
# ridge_zeros=np.int64(0), flasso_zeros=np.int64(5)

8. Логистическая регрессия. Эквивалентность подходов MLE и минимизации логистических потерь.

📌 Краткий ответ

Логистическая регрессия — это модель предсказывающая вероятность класса y = 1 :

P(y = 1 | x) = \sigma(x^\top w), \quad \sigma(z) = \frac{1}{1 + e^{-z}}

MLE: максимизация логарифма правдоподобия ⇔ минимизация log-loss (обычно для бинарной классификации) = cross-entropy-loss (обычно для мультиклассовой классификации)

$\log L(w) = \sum_i y_i \log p_i + (1 - y_i) \log(1 - p_i)$

или

$\mathcal{L}(W) = - \sum_{i=1}^{n} \sum_{k=1}^{K} p_{i, k} \cdot \log \hat{p}_{i,k}$ | обычно, $p_{i_{fix}, k}$ - ровно одна 1 и остальные нули.

🔬 Подробный разбор

📌 Вывод: MLE для логистической регрессии

Обозначим:

$y_i \in \{0, 1\}$
$p_i = \sigma(x_i^\top w)$

Правдоподобие:

L(w) = \prod_i p_i^{y_i} (1 - p_i)^{1 - y_i}

Логарифмируем:

\log L(w) = \sum_i y_i \log p_i + (1 - y_i) \log(1 - p_i)

Подставляем $p_i = \sigma(x_i^\top w)$ :

И получаем логистическую функцию потерь:

\mathcal{L}(w) = - \sum_i \left[
  y_i \log \sigma(x_i^\top w) + (1 - y_i) \log(1 - \sigma(x_i^\top w))
\right]

💻 Почему сырая линейка плоха в классификации? А лог-рег хорош?

Предлагаю разобрать пример, в котором лог-рег прекрасно абсолютно предсказывает вероятности, чем линейка не может похвастаться. Иногда нужно не просто факт класса сказать, а и вероятность!

Но дальше мы узнаем о SVM, и увидим что не обязательно приводить выход модели в диапозон [0, 1] !

# Пример: класс 0 сконцентрирован в одном месте, класс 1 — сильно растянут вправо

# Класс 0 — 50 точек около x = 0
X0 = np.random.normal(loc=0, scale=0.5, size=(50, 1))
y0 = np.zeros(50)

# Класс 1 — 50 точек с растущим x (от 10 до 500)
# X1 = np.linspace(5, 25, 10).reshape(-1, 1)
X1 = np.linspace(10, 500, 10).reshape(-1, 1)
y1 = np.ones(10)

# Объединяем
X_all = np.vstack([X0, X1])
y_all = np.concatenate([y0, y1])

# Обучаем модели
linreg = LinearRegression().fit(X_all, y_all)
logreg = LogisticRegression().fit(X_all, y_all)

# Предсказания на сетке
x_grid = np.linspace(-2, 30, 500).reshape(-1, 1)
lin_preds = linreg.predict(x_grid)
log_probs = logreg.predict_proba(x_grid)[:, 1]

# Визуализация
plt.figure(figsize=(10, 5))
plt.scatter(X0, y0, color='blue', label='Класс 0 (скученный)', alpha=0.7)
plt.scatter(X1, y1, color='orange', label='Класс 1 (удалённый)', alpha=0.9)
plt.plot(x_grid, lin_preds, color='green', linestyle='--', label='Linear Regression')
plt.plot(x_grid, log_probs, color='black', label='Logistic Regression')
plt.xlabel("x")
plt.ylabel("Предсказание / Вероятность")
plt.title("Линейная vs логистическая регрессия при удалённых объектах класса 1")
plt.ylim(-0.1, 1.1)
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

9. Многоклассовая классификация. Один-против-одного, один-против-всех, их свойства.

📌 Краткий ответ

One-vs-Rest (OvR): обучаем бинарных моделей «класс vs остальные», выбираем класс с макс. откликом.
One-vs-One (OvO): обучаем $\frac{K(K-1)}{2}$ моделей по парам классов, предсказание — по большинству голосов.

При предсказании инферяться все модели!
В One-vs-One не учитываются вероятности лишь факт победы.

🔬 Подробный разбор

📌 One-vs-Rest (OvR)

Обучение:

бинарных моделей , каждая отличает класс от остальных

Предсказание:

Вычисляем отклики $f_0(x), f_1(x), \dots, f_{K-1}(x)$
Выбираем класс с максимальным значением:
$\hat{y} = \arg\max_k f_k(x)$

Если модель выдаёт вероятности $P(y = k \mid x)$ , выбираем по ним.

📌 One-vs-One (OvO)

Обучение:

Строим классификаторы для всех пар классов:
$f_{i,j}(x) \text{ обучается на классах } i \text{ и } j$
Всего $\frac{K(K-1)}{2}$ моделей.

Предсказание:

Каждый классификатор голосует: $f_{i,j}(x) \in \{i, j\}$
Считаем число голосов за каждый класс
Итог:
$\hat{y} = \arg\max_k \text{(кол-во голосов за } k)$

Голоса — дискретные, уверенность моделей не используется.

💻 Сравнение One-vs-Rest и One-vs-One на Iris

from sklearn.datasets import load_iris
from sklearn.linear_model import LogisticRegression
from sklearn.multiclass import OneVsRestClassifier, OneVsOneClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score, confusion_matrix
import numpy as np
import pandas as pd
from IPython.display import display

# --- 1. Данные
X, y = load_iris(return_X_y=True)
X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size=0.3, random_state=0)

# --- 2. Модель
base_model = LogisticRegression(max_iter=1000)

# --- 3. One-vs-Rest (OvR)
clf_ovr = OneVsRestClassifier(base_model).fit(X_tr, y_tr)
y_pred_ovr = clf_ovr.predict(X_te)

# --- 4. One-vs-One (OvO)
clf_ovo = OneVsOneClassifier(base_model).fit(X_tr, y_tr)
y_pred_ovo = clf_ovo.predict(X_te)

# --- 5. Confusion matrices
cm_ovr = confusion_matrix(y_te, y_pred_ovr)
cm_ovo = confusion_matrix(y_te, y_pred_ovo)

print("Confusion Matrix (OvR):")
print(cm_ovr)

print("\nConfusion Matrix (OvO):")
print(cm_ovo)

# --- 6. Разбиения для OvR
ovr_split = pd.DataFrame({
    'Класс': list(range(len(clf_ovr.estimators_))),
    'Положительных': [(y_tr == k).sum() for k in range(len(clf_ovr.estimators_))],
    'Отрицательных': [(y_tr != k).sum() for k in range(len(clf_ovr.estimators_))],
    'Всего': [len(y_tr)] * len(clf_ovr.estimators_)
})

print("\nOvR — разбивка по классам:")
display(ovr_split)

# --- 7. Разбиения для OvO
ovo_pairs = [(est.classes_[0], est.classes_[1]) for est in clf_ovo.estimators_]

ovo_data = []
for a, b in ovo_pairs:
    count_a = np.sum(y_tr == a)
    count_b = np.sum(y_tr == b)
    total = count_a + count_b
    ovo_data.append({
        'Пара классов': f"{a} vs {b}",
        f"#{a}": count_a,
        f"#{b}": count_b,
        'Суммарно': total
    })

ovo_split = pd.DataFrame(ovo_data)

print("\nOvO — разбивка по парам классов:")
display(ovo_split)

# --- 8. Accuracy summary
print(f"\nOvR Accuracy: {accuracy_score(y_te, y_pred_ovr):.3f}")
print(f"OvO Accuracy: {accuracy_score(y_te, y_pred_ovo):.3f}")

Видно что датасет достаточно ~~хороший~~ игрушечный, тут и данные разделены хорошо и по классам все сбалансированно (и классов немного).

10. Метод опорных векторов. Задача оптимизации для SVM. Трюк с ядром. Свойства ядра.

📌 Краткий ответ

SVM (support vector machine) — это алгоритм решает задачу классификации ("линейная классификация"), который ищет гиперплоскость, максимально разделяющую классы с зазором (margin).

Он решает задачу максимизации отступа, то есть делает так, чтобы:

все объекты лежали как можно дальше от границы (реализуется ядром, скалярным произведением сонаправленностью <, $\hat{y}$ >)
и при этом допускались ошибки для равномерного отступа (через мягкие штрафы) (реализуется добавлением зазора=константы 1 - M).
ядра можно брать разные - не обязательно линейное

Функция потерь (hinge-loss) устроена так, чтобы:

не штрафовать объекты с отступом $\ge 1$ ,
и наказывать только те, которые «лезут» в буферную зону или ошибаются (=либо неверные, либо неуверенно правильные!):

$\mathcal{L}(w) = \frac{1}{n} \sum \max(0, 1 - y_i (w^\top x_i + b)) + \frac{\lambda}{2} \|w\|^2$

Чем, же это лучше чем просто линейная регрессия в классификации? А тем, что SVM решает задачу разделить данные, а линейная регресия старается провести через них!

🔬 Подробный разбор

📌 Модель

Классификатор:

$\hat{y}(x) = \text{sign}(w^\top x + b)$

Отступ (margin):

$M_i = y_i (w^\top x_i + b)$

Чем больше M_i , тем выше уверенность в классификации.

📌 Целевая функция (hinge loss)

SVM минимизирует:

$\mathcal{L}(w) = \frac{1}{n} \sum_{i=1}^n \max(0, 1 - y_i(w^\top x_i + b)) + \frac{\lambda}{2} \|w\|^2$

Первый член — штраф за малый отступ (ошибки или «почти ошибки»)
Второй — регуляризация (контроль за нормой )

📌 Ядровой трюк (kernel trick)

Вместо линейного $x \cdot x'$ , используем:

$K(x, x') = \langle \phi(x), \phi(x') \rangle$

→ Не нужно явно строить $\phi(x)$ , а граница может быть нелинейной.

📌 Примеры ядер

Ядро	Формула
Линейное	$K(x, x') = x^\top x'$
Полиномиальное	$K(x, x') = (x^\top x' + c)^d$
RBF (Гаусс)	$K(x, x') = \exp(-\gamma \|x - x'\|^2)$

✅ Свойства допустимого ядра (ядровой функции)

Функция K(x, x') — допустимое ядро, если оно:

Симметрична:
Положительно полуопределённая (PSD):
Для любых $x_1, \dots, x_n \in \mathbb{R}^d$ и любых весов $\alpha_1, \dots, \alpha_n \in \mathbb{R}$ выполняется:
$\sum_{i=1}^n \sum_{j=1}^n \alpha_i \alpha_j K(x_i, x_j) \ge 0$
Это значит: матрица Грама на любом наборе точек — положительно полуопределённая.

Почему это важно?

Если — валидное ядро, то по теореме Мерсера:

$K(x, x') = \langle \phi(x), \phi(x') \rangle$

для некоторого отображения $\phi(\cdot)$ в (возможно бесконечномерное) пространство признаков.

→ Это делает метод SVM с ядром линейным в этом скрытом пространстве, без явного вычисления $\phi(x)$ .

💻 Сравнения разных SVM ядер: linear vs poly vs RBF

from sklearn.datasets import make_classification
from sklearn.svm import SVC
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
import matplotlib.pyplot as plt
import numpy as np

# --- 1. Данные
X, y = make_classification(n_samples=300, n_features=2, n_redundant=0,
                           n_clusters_per_class=1, class_sep=1.0, random_state=42)
X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size=0.3, random_state=0)

# --- 2. Модели
clf_linear = SVC(kernel='linear', C=1).fit(X_tr, y_tr)
clf_rbf = SVC(kernel='rbf', gamma=1, C=1).fit(X_tr, y_tr)
clf_poly = SVC(kernel='poly', degree=3, C=1).fit(X_tr, y_tr)


# --- 3. Визуализация
def plot_decision_boundary(model, X, y, ax, title):
    h = 0.02
    x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
    y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
                         np.arange(y_min, y_max, h))
    Z = model.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)

    ax.contourf(xx, yy, Z, alpha=0.3, cmap=plt.cm.coolwarm)
    ax.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.coolwarm, edgecolors='k')
    ax.set_title(title)
    ax.set_xlabel("x₁")
    ax.set_ylabel("x₂")
    ax.grid(True)

# --- 4. Графики
fig, axes = plt.subplots(1, 3, figsize=(12, 5))
plot_decision_boundary(clf_linear, X_te, y_te, axes[0], "Линейный SVM")
plot_decision_boundary(clf_poly, X_te, y_te, axes[1], "Полиномиальный 3-й степени SVM")
plot_decision_boundary(clf_rbf, X_te, y_te, axes[2], "RBF SVM")
plt.tight_layout()
plt.show()


y_pred_linear = clf_linear.predict(X_te)
y_pred_poly = clf_poly.predict(X_te)
y_pred_rbf = clf_rbf.predict(X_te)

# Accuracy
acc_linear = accuracy_score(y_te, y_pred_linear)
acc_poly = accuracy_score(y_te, y_pred_poly)
acc_rbf = accuracy_score(y_te, y_pred_rbf)
print(f"Linear SVM Accuracy: {acc_linear:.3f}")
print(f"Polynomial SVM Accuracy: {acc_poly:.3f}")
print(f"RBF SVM Accuracy: {acc_rbf:.3f}")
# Linear SVM Accuracy: 0.944
# Polynomial SVM Accuracy: 0.911
# RBF SVM Accuracy: 0.967

Что дальше?

Учимся быстро и понятно рассказывать. Для этого проговариваем много раз. Рассказываем друзьям, либо записываем себе и слушаем.

Пока готовимся, сохраняем каверзные вопросы, на которые непросто дать верные/легкии ответы. Сначала основное, потом остальное!

Материалы

Сам список вопросов взял с одного из экзаменов
girafe.ai ~ Deep Learning School
Хендбуки Яндекс - становятся все больше и больше. Местами может быть избыточно.
SelfEdu - мегакрутой. Также, который вдохновлялся (и я тоже!) Сергеем Николенко.
MLU-EXPLAIN - на досуге можно залипнуть в интерактив.
Классический и легко написанный учебник.
Забыл одно из самых важных - LLM очень помогают набросать код и проверить гипотезу

В следующей части продолжим — будут PCA, Bias–variance tradeoff, деревья, ансамбли, бустинг, и глубокое обучение. Пока подписывайтесь и делитесь своими находками!

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15 июн. 2025 г.

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My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
16.08.25 06:53 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
16.08.25 07:01 lisared

Losing nearly 500,000 USDT to hackers was one of the most devastating experience of my life. I felt powerless as my hard-earned assets vanished into anonymous blockchain transactions until I found Agent Jasmine Lopez. Her deep expertise, tireless effort, and unwavering focus gave me hope and delivered results. She traced complex transactions, pursued every lead, and recovered a large portion of my stolen funds something I never thought possible. If you’ve lost digital assets, don’t give up. Contact Recoveryfundprovider@gmail. com WhatsApp at +{44 736-644-5035}. She turned my nightmare into a recovery story, and she could do the same for you.
16.08.25 17:05 mark

I see a lot of recommendations online and it’s already obvious there are bad eggs online who will only add to your mystery. I can only recommend one and you can reach them via mail on (zattechrecovery @ gmail c0 m ) if you need help on recovering what you lost to scammers.
17.08.25 03:33 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.08.25 03:33 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.08.25 05:22 aveasley4

I’m a California resident who was contacted by someone named “Lin” on WhatsApp. Our conversation eventually turned to cryptocurrency investments. Lin introduced me to a trading platform called CBOTBIT (https://cbotbit.com), walked me through setting up an account, and guided me on transferring funds. Under Lin’s direction, I began trading and was led to believe that my account was growing significantly. However, when I attempted to withdraw my funds, I was unable to do so — and shortly after, the website went offline entirely. I had invested over $340,000 in Bitcoin, planning to use it for my retirement. The experience was devastating, and I was at a loss for what to do next. Eventually, I came across [email protected] and decided to reach out. I followed their instructions, and within a few days, I was able to recover my original investment. I'm incredibly relieved and grateful for their assistance, and I recommend contacting them if you’re in a similar situation and need help recovering lost funds.
17.08.25 17:49 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.08.25 17:49 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.08.25 17:49 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
18.08.25 21:10 Connorhelms

I can honestly say losing my bitcoin savings was one of the darkest moments of my life. I had put everything I could into that investment, believing it would secure my future, only to wake up one day and realize the platform had vanished with all my funds. The feeling was indescribable, fear, shame, and helplessness all at once. I thought I’d never see that money again. Then I came across Alpha Spy Nest. At first, I was hesitant, I had already been deceived once, and the thought of trusting anyone else terrified me. But something about their professionalism and the way they patiently explained things gave me a little hope. For the first time in weeks, I felt like I wasn’t completely alone in the fight. They listened to my story without judgment, broke down the technical side in a way I could understand, and reassured me that there was still a chance. Watching them work was incredible. They traced every transaction, uncovered where my bitcoin had been moved, and kept me updated through every stage. It felt like they cared as much about my recovery as I did. The day they told me they had successfully recovered my lost savings, I actually cried. Seeing those funds back in my wallet felt unreal, it was like a huge weight had been lifted off my shoulders. Beyond just recovering my bitcoin, Alpha Spy Nest gave me back my peace of mind and restored a trust I thought I had lost forever. I’m forever grateful to them. If I hadn’t found Alpha Spy Nest, I’d still be stuck in regret and despair. Instead, I now share my story as proof that recovery is possible. You can also reach out to them via: Email: [email protected], WhatsApp: +15132924878‬, Telegram: https://t.me/Alphaspynest, Website: www.alphaspynest.org
18.08.25 22:17 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
18.08.25 22:17 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
19.08.25 02:26 Jacksonbash

You are not alone if you have had your bitcoins taken from your wallet or if you invested in an initial coin offering (ICO) that was a scam. I experienced the same thing. I first lost $173,000 to a fraudulent investment scam company in less than five months. I was able to get all of my money in five days thanks to a hacker my friend recommended. In order to raise awareness about these cryptocurrency criminals and do my part to minimize the number of victims, I'm speaking out. To report a victim, simply send an email to [email protected].
19.08.25 18:15 keith

RECOVER FROM CRYPTO SCAMS WITH THE HELP OF BONES RECOVERY BITCOIN EXPERT If someone needs to recover cryptocurrency that has been lost to wallet hackers, internet scammers, or BTC transferred to the wrong address, I suggest BONES RECOVERY BITCOIN, a very trustworthy recovery organization . Simply presenting my case to the expert and supplying the necessary data allowed BONES RECOVERY BITCOIN to assist me in recovering my Bitcoin. It's a relief that I recovered this much after losing considerably more to the fraudulent broker I initially put my trust in. Because we will inevitably make mistakes, we can never be diligent enough. If you have lost money to cryptocurrency scams, I strongly advise getting in touch with BONES RECOVERY BITCOIN. Contact address WhatsApp....‪+1-60-621-024-64‬ Email [email protected]
19.08.25 18:54 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
19.08.25 18:54 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
19.08.25 18:54 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
20.08.25 12:01 Official

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20.08.25 17:00 lisared

Few months ago I experienced one of the most devastating moments of my life €300k was stolen by hackers . When my money was stolen I felt hopeless, until I was introduced to Agent Jasmine Lopez her expertise and dedication gave me peace of mind. She skillfully traced complex transactions and tracked down the scammers, which would have been impossible for me to do on my own. Thanks to her tireless efforts, I was able to recover a significant portion of my lost funds. If you've fallen victim of hackers, I highly recommend reaching out to her. You can contact her via email at Recoveryfundprovider@gmail. com WhatsApp at +{44 736-644-5035}. Her attention to detail and commitment to her work are truly impressive. Don't hesitate to reach out her expertise could be the key to recovering your lost funds.
20.08.25 20:42 vallatjosette

My Wild Ride: How a Wizard Hilton Cyber Tech Helped Me Recover Lost Bitcoin of 103,000 It all started when I had the misfortune of misplacing the digital wallet containing my substantial cryptocurrency holdings - a staggering 103,000 bitcoins. I had amassed this sizable fortune over the years through strategic investments and careful trading, but in a moment of carelessness, the private keys to my digital wallet had vanished. Panic set in as I grappled with the gravity of my situation - those bitcoins, worth millions at the time, were effectively lost to the ether, inaccessible and seemingly unrecoverable. Just when I had resigned myself to the devastating financial blow, a chance encounter with a self-proclaimed "digital wizard" Wizard Hilton Cyber Tech presented a glimmer of hope. This enigmatic individual, who operated in the shadowy corners of the crypto underworld, claimed to possess the arcane knowledge and skills necessary to retrieve my lost digital wealth. Intrigued and desperate, I put my skepticism aside and entrusted this mysterious wizard with the task. What followed was a wild, suspenseful journey into the depths of blockchain technology and cryptography, as the wizard navigated complex algorithms, exploited vulnerabilities, and pieced together the puzzle of my missing private keys. After days of intense effort, Wizard Hilton Cyber Tech emerged triumphant, having successfully recovered the entirety of my 103,000 bitcoin stash. The sheer relief and elation I felt in that moment was indescribable, as I regained access to my small digital fortune and was able to secure my financial future. This harrowing experience taught me the invaluable lesson of never taking the security of my cryptocurrency holdings for granted, and the importance of always maintaining the utmost diligence when it comes to protecting one's digital wealth. Email: wizardhiltoncybertech ( @ ) gmail (. ) com OR support ( @ ) wizardhiltoncybertech (.) com WhatsApp number +18737715701 Thanks.
21.08.25 01:54 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
21.08.25 01:54 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
21.08.25 01:54 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
21.08.25 14:56 elainemurray

E.M.A.I.L. [email protected] W.h.a.t.s.A.p.p. +1(561)(726)(3697) It all began with an Instagram advertisement. A man presented himself as a cryptocurrency investment coach, showcasing a luxurious lifestyle and screenshots of substantial profits. He claimed his trading algorithm could double any investment in a week. Curious, I decided to reach out to him. He said the minimum investment was $50,000 and sent me a link to a platform that looked legitimate. At first, everything seemed promising. My balance increased steadily, charts showed growth, and I felt excited. When I tried to withdraw the money, the system blocked the transaction and demanded a release fee of $15,000. I paid it, but my account was soon marked under review, and the coach stopped responding. I realised I had been scammed. Desperate, I turned to Techy Force Cyber Retrieval. From the first consultation, they carefully reviewed my case and assured me the funds could be traced. They explained how they would track the wallet addresses and follow the path of the stolen money. Their clear guidance made me feel confident. Over the next few weeks, Techy Force Cyber Retrieval kept me updated on every step. They traced the transactions. Their persistence and expertise were obvious, and I could see real progress. Even when the process felt slow, Techy Force Cyber Retrieval maintained clear communication. They explained each action and why it mattered. Their careful attention made the ordeal manageable and reassuring. A month later, thanks to Techy Force Cyber Retrieval, I was able to recover 80% of my money and have it safely returned to my bank account. Relief and gratitude overwhelmed me. What started as a tempting opportunity had turned into a stressful ordeal, but Techy Force Cyber Retrieval transformed it into a successful resolution.
21.08.25 21:17 monte5757

I went through one of the most painful experiences of my life I lost over $850,000 to scammers. They had no mercy,things got so bad that I even sold some of my properties just to keep up with their demands. At one point, I felt completely hopeless and trapped. But everything changed when I came across a legit recovery agent who actually helped me recover my funds and return them safely to my wallet. It was like getting my life back. If you’ve ever been scammed, please don’t give up. Reach out to Recoveryfundprovider [at] gmail [dot] com WhatsApp at +{44 736-644-5035}.she’s professional, reliable, and truly knows how to get results. I’m genuinely grateful I found her, and I believe you’ll thank me later too.
22.08.25 08:00 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
22.08.25 08:00 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
22.08.25 08:00 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
23.08.25 05:11 ramiroalcazar

A hacker skillfully impersonated one of our clients’ trusted suppliers and manipulated their finance department into transferring $180,000 worth of Bitcoin. The request appeared authentic, reinforced by falsified documents and meticulously crafted communication that mirrored the supplier’s established style. By the time the company uncovered the deception, the funds had already been funneled through numerous digital wallets. When they appealed to their bank for assistance, they were told recovery was impossible since cryptocurrency transactions are irreversible. The company suddenly faced the prospect of financial ruin. Confronted with this devastating loss, the client sought a specialized solution and turned to Techy Force Cyber Retrieval. From the initial consultation, our team demonstrated that hope remained. Unlike the bank, which dismissed their plea, Techy Force Cyber Retrieval meticulously analyzed every aspect of the fraud and assured the client that our blockchain specialists had the tools to trace and potentially reclaim the stolen assets. Our investigation began with a comprehensive audit of the fraudulent transactions. Using advanced blockchain forensics, Techy Force Cyber Retrieval’s analysts traced the stolen Bitcoin across a labyrinth of wallets and exchanges. Every development was documented with precision, and regular updates were delivered to the client, ensuring transparency and trust. This combination of technical mastery and clear communication provided reassurance during an otherwise overwhelming crisis. After persistent tracking and strategic intervention, Techy Force Cyber Retrieval achieved a remarkable outcome. From the original $180,000 that had been siphoned away, our team successfully recovered the equivalent of $160,000 in USDT. This restitution enabled the company to meet payroll obligations, stabilize its operations, and avert what had seemed like an inevitable collapse. What distinguished Techy Force Cyber Retrieval in the eyes of the client was not only our technical expertise but also our dedication and professionalism. We approached the case with urgency, maintained open communication at every stage, and treated the recovery effort with the utmost seriousness. At a moment when the client felt powerless, Techy Force Cyber Retrieval restored both their assets and their confidence. Now, victims of cryptocurrency fraud do not have to accept total loss. With the right expertise, recovery is achievable. Techy Force Cyber Retrieval stands as proof that even in situations deemed hopeless, we can deliver tangible results and provide businesses and individuals with a genuine second chance. CONSULT TECHY FORCE CYBER RETRIEVAL FOR A GREAT SOLUTION RECOVERY......... WHATSAPP.......... +15617263697 WEBSITE......... https://techyforcecyberretrieval.com
24.08.25 01:05 samshaffer

Have been on the quest for a way to recover my $195,000 from a forex broker. I was fortunate to meet Darek at ([email protected]) through a friend who was recommended as the best crypto recovery specialist he was the one who assisted me and restore my money back to my atomic wallet. I did reach him at [email protected] and it was an amazing experience. Never knew there was an expert who could trace back crypto until I met this great team. Don’t think twice, get connected with the right personnel now to avoid been fooled again..
24.08.25 06:32 amy

I have lost all hope to recover my investment in pragmatic trade which I lost $125,000 in the process of investment. I'm here to say thank you to anthony davies for being a man of your word got my funds recovered back plus a bonus within a week of working with [email protected] I hope people make use of this opportunity as well and don't give up on getting your funds back. is also available on Telegram: @anthonydavies01
24.08.25 17:13 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.08.25 17:13 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.08.25 17:13 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.08.25 18:39 nelly young

Getting your USDC stolen feels like the ground has been pulled out from under you. It’s not just about the money you’ve been violated, and your security is at risk. And since crypto lives on the blockchain, there’s no bank to call and no quick refund. That’s why you need someone who knows exactly what to do. Agent Jasmine Lopez has helped countless victims trace stolen USDC and lock down their accounts before more damage happens. Time matters reach her today at [email protected] WhatsApp at +44 736-644-5035 and take the first step toward getting your funds and peace of mind back.
24.08.25 23:56 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: Recoverycapital @fastservice. com Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.08.25 23:56 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: Recoverycapital @fastservice. com Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.08.25 23:56 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: Recoverycapital @fastservice. com Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.08.25 00:55 vallatjosette

My Wild Ride: How a Wizard Hilton Cyber Tech Helped Me Recover Lost Bitcoin of 103,000 It all started when I had the misfortune of misplacing the digital wallet containing my substantial cryptocurrency holdings - a staggering 103,000 bitcoins. I had amassed this sizable fortune over the years through strategic investments and careful trading, but in a moment of carelessness, the private keys to my digital wallet had vanished. Panic set in as I grappled with the gravity of my situation - those bitcoins, worth millions at the time, were effectively lost to the ether, inaccessible and seemingly unrecoverable. Just when I had resigned myself to the devastating financial blow, a chance encounter with a self-proclaimed "digital wizard" Wizard Hilton Cyber Tech presented a glimmer of hope. This enigmatic individual, who operated in the shadowy corners of the crypto underworld, claimed to possess the arcane knowledge and skills necessary to retrieve my lost digital wealth. Intrigued and desperate, I put my skepticism aside and entrusted this mysterious wizard with the task. What followed was a wild, suspenseful journey into the depths of blockchain technology and cryptography, as the wizard navigated complex algorithms, exploited vulnerabilities, and pieced together the puzzle of my missing private keys. After days of intense effort, Wizard Hilton Cyber Tech emerged triumphant, having successfully recovered the entirety of my 103,000 bitcoin stash. The sheer relief and elation I felt in that moment was indescribable, as I regained access to my small digital fortune and was able to secure my financial future. This harrowing experience taught me the invaluable lesson of never taking the security of my cryptocurrency holdings for granted, and the importance of always maintaining the utmost diligence when it comes to protecting one's digital wealth. Email: wizardhiltoncybertech ( @ ) gmail (. ) com OR support ( @ ) wizardhiltoncybertech (.) com WhatsApp number +18737715701 Thanks.
25.08.25 05:14 samshaffer

Have been on the quest for a way to recover my $195,000 from a forex broker. I was fortunate to meet Darek at ([email protected]) through a friend who was recommended as the best crypto recovery specialist he was the one who assisted me and restore my money back to my atomic wallet. I did reach him at [email protected] and it was an amazing experience. Never knew there was an expert who could trace back crypto until I met this great team. Don’t think twice, get connected with the right personnel now to avoid been fooled again..
26.08.25 10:14 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.08.25 10:14 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.08.25 10:14 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.08.25 23:59 floridaberna

It began as an entirely ordinary afternoon when an unexpected message appeared in my Facebook inbox. The sender was a woman I had never encountered. She introduced herself with warmth and courtesy, explaining that her late husband had been deeply invested in Bitcoin before his sudden passing. According to her narrative, he had left behind a vast fortune in cryptocurrency. However, due to intricate international banking regulations and legal entanglements, she was unable to access the funds without external assistance. Her words carried an air of urgency yet also sincerity. She claimed she had come across my profile in a cryptocurrency discussion forum and believed I might be the right person to help. The obstacle she faced was a set of legal fees amounting to $25,000. Once those costs were paid, she assured me the Bitcoin would be unlocked and a generous portion would be mine in gratitude. Against my better instincts, I allowed myself to be persuaded. She provided what appeared to be legitimate documents and even screenshots of supposed legal correspondence. The level of detail made her story feel authentic. After several exchanges, I transferred the $25,000.Almost immediately, her demeanor shifted. Responses became sporadic and vague. Within days, communication ceased entirely. My optimism dissolved into dread as I recognized the truth. I had been deceived. Refusing to surrender, I searched for solutions and discovered TECHY FORCE CYBER RETRIEVAL, a firm specializing in tracing and reclaiming stolen cryptocurrency. Their team outlined a meticulous plan to track the blockchain trail, identify the sequence of wallets involved, and coordinate with local authorities to freeze the assets before they disappeared into the labyrinth of the crypto underworld. Time was critical. In the volatile realm of digital currency, stolen funds can be laundered through countless transactions within hours. Yet TECHY FORCE CYBER RETRIEVAL pursued each lead with relentless precision. They provided regular progress updates and explained how every crypto transaction leaves a digital footprint, no matter how deeply it is buried. Weeks later, the breakthrough came. The fraudulent account was located, the illicit funds were flagged, and to my immense relief, I recovered 100% of my stolen money. This left me with an invaluable lesson. The internet is full of opportunists who prey on trust and desperation. But should you ever fall victim, know that there are experts like TECHY FORCE CYBER RETRIEVAL who can help you reclaim what is rightfully yours. MAil support (@) techyforcecyberretrieval (.) com WhatsApp +1 561 726 369 7 Website ht tp s : / / techy force cyber retrieval . com
27.08.25 17:24 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.08.25 17:24 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.08.25 17:24 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.08.25 20:27 maximeden68

Top Crypto Bitcoin Wallet Recovery Services Contact iFORCE HACKER RECOVERY I wish to express my sincere gratitude to iForce Hacker Recovery for their exceptional service in recovering my lost bitcoin. Their expertise and professionalism were evident throughout the process, providing me with reassurance during a challenging time. The team's dedication to client satisfaction and their effective strategies were instrumental in resolving my issue. I highly recommend their services to anyone facing similar challenges. Thank you, iForce Hacker Recovery. Contact iForce Hacker Recovery: Email: iforcehk @ consultant. com WhatsApp: +1 (240) 803-3706 Website: iforcehackers. com/
27.08.25 21:21 dbeverly

One morning I received an email that looked like it came from my cryptocurrency exchange, OKX. The subject warned: Suspicious activity detected and urged me to log in via a link. The message seemed authentic — perfect logos, formatting, even the sender’s address. My pulse spiked and I clicked. The site that opened was indistinguishable from OKX’s homepage. Convinced it was real, I entered my username and password. Moments later, dread set in: my account was emptied. $12,500 in Bitcoin was gone. I called OKX, hoping for a reversal, but the representative explained transfers were irreversible. Desperate, I turned to GRAYWARE TECH SERVICE. From the first call, their professionalism was clear. They carefully examined my case, tracing the stolen Bitcoin across the blockchain. They identified the destination wallets and mapped every move the hackers made. Their regular updates turned fear into cautious optimism. Acting swiftly, GRAYWARE coordinated with exchanges along the path of the stolen funds, freezing assets before they could vanish. Their vigilance and expertise kept me informed and reassured. After two tense weeks, the breakthrough came: my full $12,500 was recovered and returned to my OKX account. What began as a nightmare became a success thanks to GRAYWARE TECH SERVICE’s relentless determination. They didn’t just recover my money — they restored my confidence in digital security. Contact: WhatsApp: +1 858 275 9508 Website: https://graywaretechservice.com Email: [email protected]
28.08.25 10:08 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.08.25 10:08 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.08.25 10:08 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.08.25 13:50 Maureensels

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28.08.25 13:50 Maureensels

STEPS TO RECOVERING MONEY FROM A CRYPTO INVESTMENT SCAM CONTACT WIZARD LARRY RECOVERY EXPERTS Are you trying to find a means to get your other cryptocurrency, including Bitcoin, back from scammers? Stop searching! Call or text +1 (616) - (292) - (4789) or send a mail to (WIZARDLARRY(@)MAIL. C OM) is the greatest Scammed Crypto Recovery Agency I've seen on Google Earth. I'm delighted I made the brave decision to get in touch with them. In a matter of hours, all of the cryptocurrency that I had stolen was returned to my Coin Base wallet. For assistance with their strategies, I will advise you all to get in touch with their customer service. You will thank me later. Website... Wizardlarryrecovery. com Email [email protected] o m
28.08.25 16:31 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.08.25 16:31 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.08.25 19:17 leticiazavala

Earlier this year, I found what looked like an unbeatable offer on first-class airline tickets through an online travel agency. They advertised heavily discounted fares for international travel for only 0.11 BTC, which was worth around 7300 USD at the time. The only condition was that payment had to be made in Bitcoin. The website looked professional, had convincing reviews, and even offered live chat support. After some hesitation, I decided to go ahead with the booking. Two days later, I received an email from the airline saying my reservation had been canceled. I went back to the agency’s website only to find it had disappeared. Their customer support was gone, and their social media accounts had vanished. That was when I realized I had been scammed. I thought my Bitcoin was lost for good. Unlike a credit card transaction, there was no way to reverse it. A friend recommended a company called Techy Force Cyber Retrieval that specializes in tracking and recovering stolen crypto. I reached out not expecting much. To my surprise, their team responded quickly. I sent them the transaction details, and they immediately began tracing the movement of the 0.11 BTC. They followed the funds through multiple wallets and discovered the Bitcoin had ended up at a large exchange known for cooperating in fraud investigations. Techy Force Cyber Retrieval worked fast. They submitted the evidence to the exchange and requested that the wallet be frozen. Over the next few weeks, they handled all communication and submitted the necessary documentation. Just under three weeks later, the exchange approved the release of my funds. I was stunned when I saw the 0.11 BTC back in my wallet. I had lost hope, but Techy Force Cyber Retrieval delivered. They were professional, honest, and transparent throughout the entire process. If you have been scammed in a crypto deal, do not assume the money is gone forever. With the right help, it is possible to trace and recover stolen assets. Techy Force Cyber Retrieval gave me a second chance, and I would not hesitate to recommend them to anyone who finds themselves in a similar situation. FOR SERVICE HELP Email: [email protected] [email protected] CALL +15617263697
29.08.25 09:20 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.08.25 09:20 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.08.25 09:20 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
30.08.25 01:40 Moises Velez

In a single transaction, my Coinbase wallet was destroyed. I was at a loss as to what to do and was unable to contact Coinbase support Teams. This transaction resulted in the complete depletion of my Ethereum and Bitcoin. I was not the individual in question, and I required assistance after losing approximately $821,000. I visited the police station to submit a report, but they were also unable to provide any assistance. A gentleman approached me at the stiction and presented me with a note that included an email address (recoveryhacker101[at]gmail[dot]com). He informed me that this recovery company could be of assistance. Upon contacting them and submitting all necessary documentation within 72 hours, I received a letter stating that she had successfully recovered all of my funds and identified the individuals responsible for the criminal activity. I would like to inform everyone that it is feasible to retrieve their funds provided that they correspond with the appropriate individual and adhere to the prescribed procedures.
31.08.25 14:19 jack118

In 2018, Marie assisted in the recovery of stolen bitcoin. The service was excellent. The coins were stolen by hackers, creating a nightmare. Marie was suggested by a friend. Contact her at [email protected] and @MARIE_CONSULTANCY on Telegram or WhatsApp at +1 7127594675. She was responsible for recovering Bitcoin. The trading goes on.
31.08.25 23:14 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
31.08.25 23:14 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
31.08.25 23:14 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
01.09.25 04:55 Maurice Cherry

Through Hackrontech recovery, Bitcoin scam victims can retrieve their money. I recommed hackrontech to anyone who has fallen victim to a scam and has been looking for methods and techniques to recover their lost cryptocurrency or wallets. Hackrontech Recovery is a reliable cryptocurrency recovery firm that assists victims in recovering their stolen cryptocurrency and offers secure solutions to protect your wallets from online scammers. I must admit that I was deeply melancholy and had given up on life until these experts could restore my 4.1 BTC to my wallet. If you’ve lost your cryptocurrency and you are helpless about it, contact hackrontech Recovery to get your money back. Email : hackrontech @gmail.com One key aspect that makes hackrontech Recovery stand out is its focus on providing secure solutions to protect wallets from online scammers. It’s not just about recovering lost funds; it’s also about preventing future incidents and ensuring that clients’ digital assets are safeguarded against potential threats. This proactive approach demonstrates their commitment to the long-term financial security of their clients. Furthermore, for individuals who have lost their cryptocurrency and are feeling helpless, reaching out to hackrontech Recovery could be a turning point in their situation. The reassurance that they are legitimate for seeking help and recovering lost funds can provide much-needed relief and a sense of empowerment. hackrontech Recovery as a reliable cryptocurrency recovery firm is certainly well-founded. Their ability to assist scam victims in recovering stolen cryptocurrency, their focus on providing secure solutions, and their commitment to supporting clients through challenging situations make them a valuable resource for individuals navigating the complex world of digital currencies. If you or someone you know has fallen victim to a cryptocurrency scam, contacting hackrontech Recovery could be the first step towards reclaiming lost funds and regaining peace of mind. Contact info; email: hackrontech @gmail.com
01.09.25 11:06 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
01.09.25 11:07 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
01.09.25 16:41 Anitastar

Wizard Hilton Cyber Tech's strategic approach to Bitcoin recovery represents a mutually beneficial collaboration that offers valuable advantages for all involved. At the core of this innovative partnership is a shared commitment to leveraging cutting-edge technology and expertise to tackle the increasingly complex challenges of cryptocurrency theft and loss. By combining Wizard Hilton's world-class cybersecurity capabilities with the deep industry insights and recovery methodologies of Cyber Tech, this alliance is poised to revolutionize the way individuals and organizations safeguard their digital assets. Through a meticulous, multi-layered process, the team meticulously analyzes each case, employing advanced forensic techniques to trace the flow of stolen funds and identify potential recovery avenues. This rigorous approach not only maximizes the chances of successful Bitcoin retrieval, but also provides invaluable intelligence to enhance future security measures and prevention strategies. Importantly, the collaboration is built on a foundation of trust, transparency, and a genuine concern for the well-being of clients, ensuring that the recovery process is handled with the utmost care and discretion. As the cryptocurrency landscape continues to evolve, this strategic alliance between Wizard Hilton Cyber Tech stands as a shining example of how industry leaders can come together to safeguard digital assets, protect victims of cybercrime, and pave the way for a more secure and resilient cryptocurrency ecosystem. Email : wizardhiltoncybertech ( @ ) gmail (. ) com OR support ( @ ) wizardhiltoncybertech (.) com WhatsApp number +18737715701 Thanks.
01.09.25 17:03 WILLER GOODY

Don’t be misled by the countless stories you come across online many of them are unreliable and can easily steer you in the wrong direction. I personally tried several so-called recovery services, only to end up frustrated and disappointed every single time. But everything changed when I finally connected with a true tech professional who genuinely knows what they’re doing. Instead of wasting time and energy with unskilled hackers who make empty promises, it’s far better to work with a proven expert who can actually recover your stolen or lost cryptocurrency, including Bitcoins. [email protected] is, without a doubt, one of the most trustworthy and skilled blockchain specialists I’ve ever come across. If you’ve lost money to scammers, don’t give up. Reach out to their email today and take the first step toward getting your coins back. You can also contact them at +44 736-644-5035.
02.09.25 23:12 [email protected]

Sylvester Bryant has recovered over £151,000 in lost cryptocurrency. You can reach him for assistance via email at Yt7cracker@gmail. com. For direct communication, Sylvester Bryant is available on WhatsApp at +1 512 577 7957. This service proved invaluable when other recovery methods had failed. The money was recovered quickly and effectively. My financial situation was dire prior to this. This recovery has restored my financial stability. This reliable support was crucial during a difficult time. Mr. Bryant's skill in retrieving lost funds is remarkable.
03.09.25 07:17 Fabian3

Scammers have ruined the forex trading market, they have deceived many people with their fake promises on high returns. I learnt my lesson the hard way. I only pity people who still consider investing with them. Please try and make your researches, you will definitely come across better and reliable forex trading agencies that would help you yield profit and not ripping off your money. Also, if your money has been ripped-off by these scammers, you can report to a regulated crypto investigative unit who make use of software to get money back. They helped me recover my scammed funds back to me If you encounter with some issue make sure you contact ([email protected]) they're recovery expert and a very effective and reliable .
04.09.25 02:11 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
04.09.25 02:11 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
04.09.25 02:45 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
04.09.25 16:24 Melbourne

Sylvester Bryant has recovered over £151,000 in lost cryptocurrency. You can reach him for assistance via email at Yt7cracker@gmail. com. For direct communication, Sylvester Bryant is available on WhatsApp at +1 512 577 7957. This service proved invaluable when other recovery methods had failed. The money was recovered quickly and effectively. My financial situation was dire prior to this. This recovery has restored my financial stability. This reliable support was crucial during a difficult time. Mr. Bryant's skill in retrieving lost funds is remarkable.
04.09.25 18:11 WILLER GOODY

Don't fall for fake recovery scams online. Many people promise to help you get back lost crypto. They often just make excuses or don't deliver. This leads to more disappointment and lost hope. After many bad experiences, I finally found a real expert. They were professional and knew what they were doing. This person actually recovered my stolen coins. They gave me peace of mind back. If you lost crypto, contact them at [email protected] WhatsApp at +44 736-644-5035. Don't waste your time with others. They can help you get your money back.
05.09.25 08:14 Amostampari

How can I Recover My Lost Btc, Usdt - Wizard Larry Recovery Experts. Get Your Stolen Crypto Coins Back By Hiring A Hacker || I Can't Get Into My USDT? Account, It Seems Like I Was Hacked || Do You Need A Bitcoin Recovery Expert? Getting Lost, Stolen Crypto, or Hacked? How can I retrieve cryptocurrency from a con artist? Do I need a hacker to get my money back? Getting in dealing with a reputable business like Wizard Larry Recovery Experts could help you get your money back if you can't access your USDT account or have lost Bitcoin or NFT as a result of hacking or scams. For additional support and direction on your particular circumstance, it is advised that you get in touch with them at the address below ADDRESS Website... https://larrywizard43.wixsite.com/wizardlarry OR www.wizardlarryrecovery. com Email... wizardlarry@mail. com WhtsApp or call,.. +447 (311) 146 749
05.09.25 15:39 micheal1219

Losing USDT can be upsetting. This stablecoin usually stays close to the dollar's value. However, mistakes happen. Bugs in code, scams, or sending funds to the wrong place can cause losses. It might feel like the money is gone forever. But often, recovery is possible. Contact Marie at [email protected]. You can also reach her on Telegram at @marie_consultancy or WhatsApp at +17127594675.
06.09.25 09:21 Young Felix

[email protected] will Help you Recovery your Scammed Funds.
06.09.25 09:22 Young Felix

[email protected] will Help you Recovery your Scammed Funds. I just had to share my experience with Intel Fox Recovery Services. Initially, I was unsure if it would be possible to recover my BTC, however, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. Here is another caution; not all recovery services are legit. I personally lost 3 BTC from my Binance account due to a deceptive platform. If you happen to have suffered a similar loss, consider INTEL FOX RECOVERY SERVICES. Their services not only showcase a highly mannerism of professionalism but also effectiveness of how they handle and assist their clients. Therefore, I highly recommend their services to anyone seeking assistance in recovering their stolen BTC.
06.09.25 18:52 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
06.09.25 18:52 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
08.09.25 14:26 bajo171

Recovery experts and lawyers work together to get your stolen money back. They find lost assets. Lawyers guide you through legal steps. Watch out for scam signs. Be careful of offers promising big profits with no risk. Don't let anyone rush your investment decisions. Marie can help you get back lost Bitcoin. She also helps stop future scams. Contact her on WhatsApp at +1 7127594675. You can also email her at [email protected] or reach her on Telegram at @Marie_consultancy.
08.09.25 18:04 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
08.09.25 18:04 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
08.09.25 19:21 DAVEortega1010

Be wary of fraudulent cryptocurrency recovery services. Many promise to recover your lost digital currency. These services often provide excuses or fail to deliver any results. This only adds to your distress. After several unsuccessful attempts with others, I discovered a genuine expert. This individual was highly capable and provided excellent assistance. They successfully recovered my stolen cryptocurrency. I was finally able to find peace of mind. If you have lost crypto, you should contact them. talk to [email protected] for help. You can also send a text message via WhatsApp to +447366445035, Stop losing time on scams. They can help you get your money back.
02:34 wendytaylor015

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02:34 wendytaylor015

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02:34 wendytaylor015

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11:48 Moises Velez

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15:05 patricialovick86

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15:05 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15:05 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1