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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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A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
14.11.25 10:39 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
14.11.25 12:12 daisy

i Lost $200,000 to a phishing scam in 2022. Funds went to a mixer service. Davies traced 70% through Ethereum layers. He teamed with an exchange to freeze the rest. i got $140,000 back in six months. Hiring Davies means clear steps. You share details. He checks facts. Then, the hunt begins. Expect ups and downs, but his plan keeps it steady. you can reach out to him by sending an email to anthonydaviestech {@} gmail com
14.11.25 15:07 caridad

Perth Family Saved After $400K Crypto Scam Our family in Perth, WA invested through what we thought was a trusted platform but ended up being a fraudulent investment scheme. We lost nearly AUD 420,000 worth of BTC and USDT. Luckily, a friend recommended Bitreclaim.com. Their 24/7 customer support assigned us a smart contract audit specialist who asked for wallet addresses and transaction hashes. With their forensic blockchain trace, they recovered over 5.1 BTC directly into our hardware wallet. For Perth investors: don’t give up hope. Submit a case at Bitreclaim.com immediately. Their professionalism and success rate in Australia is unmatched.
14.11.25 18:33 justinekelly45

FAST & RELIABLE CRYPTO RECOVERY SERVICES Hire iFORCE HACKER RECOVERY I was one of many victims deceived by fake cryptocurrency investment offers on Telegram. Hoping to build a retirement fund, I invested heavily and ended up losing about $470,000, including borrowed money. Just when I thought recovery was impossible, I found iForce Hacker Recovery. Their team of crypto recovery experts worked tirelessly and helped me recover my assets within 72 hours, even tracing the scammers involved. I’m deeply thankful for their professionalism and highly recommend their services to anyone facing a similar situation. Website: ht tps://iforcehackers. co m WhatsApp: +1 240-803-3706 Email: iforcehk @ consultant. c om
14.11.25 20:56 juliamarvin

Firstly, the importance of verifying the authenticity of online communications, especially those about financial matters. Secondly, the potential for recovery exists even in cases where it seems hopeless, thanks to innovative services like TechY Force Cyber Retrieval. Lastly, the cryptocurrency community needs to be more aware of these risks and the available solutions to combat them. My experience serves as a warning to others to be cautious of online impersonators and never to underestimate the potential for recovery in the face of theft. It also highlights the critical role that professional retrieval services can play in securing your digital assets. In conclusion, while the cryptocurrency space offers unparalleled opportunities, it also presents unique challenges, and being informed and vigilant is key to navigating this landscape safely. W.h.a.t.s.A.p.p.. +.15.6.1.7.2.6.3.6.9.7. M.a.i.l T.e.c.h.y.f.o.r.c.e.c.y.b.e.r.r.e.t.r.i.e.v.a.l.@.c.o.n.s.u.l.t.a.n.t.c.o.m. T.e.l.e.g.r.a.m +.15.6.1.7.2.6.3.6.9.7
15.11.25 12:47 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
15.11.25 14:39 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
15.11.25 14:39 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
15.11.25 15:31 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
15.11.25 15:52 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
16.11.25 14:43 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
16.11.25 14:44 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
16.11.25 20:38 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
17.11.25 03:24 johnny231

INFO@THEBARRYCYBERINVESTIGATIONSDOTCOM is one of the best cyber hackers that i have actually met and had an encounter with, i was suspecting my partner was cheating on me for some time now but i was not sure of my assumptions so i had to contact BARRY CYBER INVESTIGATIONS to help me out with my suspicion. During the cause of their investigation they intercepted his text messages, social media(facebook, twittwer, snapchat whatsapp, instagram),also call logs as well as pictures and videos(deleted files also) they found out my spouse was cheating on me for over 3 years and was already even sending nudes out as well as money to anonymous wallets,so i deciced to file for a divorce and then when i did that i came to the understanding that most of the cryptocurrency we had invested in forex by him was already gone. BARRY CYBER INVESTIGATIONS helped me out through out the cause of my divorce with my spouse they also helped me in retrieving some of the cryptocurrency back, as if that was not enough i decided to introduce them to another of my friend who had lost her most of her savings on a bad crytpo investment and as a result of that it affected her credit score, BARRY CYBER INVESTIGATIONS helped her recover some of the funds back and helped her build her credit score, i have never seen anything like this in my life and to top it off they are very professional and they have intergrity to it you can contact them also on their whatsapp +1814-488-3301. for any hacking or pi jobs you can contact them and i assure you nothing but the best out of the job
17.11.25 11:26 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
17.11.25 11:27 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
19.11.25 01:56 VERONICAFREDDIE809

Earlier this year, I made a mistake that changed everything. I downloaded what I thought was a legitimate trading app I’d found through a Telegram channel. At first, everything looked real until I tried to withdraw. My entire investment vanished into a bot account, and that’s when the truth hit me: I had been scammed. I can’t describe the feeling. It was as if the ground dropped out from under me. I blamed myself. I felt stupid, ashamed, helpless every painful emotion at once. For a while, I couldn’t even talk about it. I thought no one would understand. But then I got connected to the best female expert AGENT Jasmine Lopez,,( [email protected] ) ,She didn’t brush me off or judge me. She took my fear seriously. She followed leads I didn’t even know existed, and identified multiple off-chain indicators and wallet clusters linked to the scammer network, she helped me understand what had truly happened behind the scenes. For the first time since everything fell apart, I felt hope. Hearing that other people students, parents, hardworking people had been targeted the same way made me realize I wasn’t alone. What happened to us wasn’t stupidity. It was a coordinated attack. We were prey in a system built to deceive. And somehow, through all the chaos, Agent Jasmine stepped in and shined a light into the darkest moment of my life. I’m still healing from the experience. It changed me. But it also reminded me that even when you think you’re at the end, sometimes a lifeline appears where you least expect it. Contact her at [email protected] WhatsApp at +44 736-644-5035.
19.11.25 08:11 JuneWatkins

I’m June Watkins from California. I never thought I’d lose my life savings in Bitcoin. One wrong click, a fake wallet update, and $187,000 vanished in seconds. I cried for days, felt stupid, ashamed, and completely hopeless. But God wouldn’t let me stay silent or defeated. A friend sent me a simple message: “Contact Mbcoin Recovery Group, they specialize in this.” I was skeptical (there are so many scammers), but something in my spirit said “try.” I reached out to Mbcoin Recovery Group through their official site and within minutes their team responded with kindness and clarity. They walked with me step by step, and stayed in constant contact. Three days later, I watched in tears as every single Bitcoin returned to my wallet, 100% recovered. God turned my mess into a message and my shame into a testimony! If you’ve lost crypto and feel it’s gone forever, don’t give up. I’m living proof that recovery is possible. Thank you, Mbcoin Recovery Group, and thank You, Jesus, for never leaving me stranded. contact: (https://mbcoinrecoverygrou.wixsite.com/mb-coin-recovery) (Email: [email protected]) (Call Number: +1 346 954-1564)
19.11.25 08:26 elizabethmadison

My name is Elizabeth Madison currently living in New York. There was a time I felt completely broken. I had trusted a fraudulent bitcoin investment organization, who turned out to be a fraudster. I sent money, believing their sweet words and promises on the interest rate I will get back in return, only to realize later that I’ve been scammed. On the day of withdrawal there was no money in my account. The pain hit deep. I couldn’t sleep, I kept asking myself how I could have been so careless, meanwhile my mom was battling with a stroke and the expenses were too much. For days, I cried and blamed myself. The betrayal, the disappointment and my mom's health issues all of this stress made me want to give up on life. But one day, I decided that sitting in pain wouldn’t solve anything. I picked myself up and chose to fight for what I lost then I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how he helped people recover their funds from online fraud. I emailed all the transactions and paperwork I had with the fraudulent organization and they helped me recover all my lost money in just five days. If you have ever fallen victim to scammers, contact GREAT WHIP RECOVERY CYBER SERVICES to help you recover every penny you have lost. (Text +1(406)2729101) (Email [email protected])
19.11.25 08:27 elizabethmadison

My name is Elizabeth Madison currently living in New York. There was a time I felt completely broken. I had trusted a fraudulent bitcoin investment organization, who turned out to be a fraudster. I sent money, believing their sweet words and promises on the interest rate I will get back in return, only to realize later that I’ve been scammed. On the day of withdrawal there was no money in my account. The pain hit deep. I couldn’t sleep, I kept asking myself how I could have been so careless, meanwhile my mom was battling with a stroke and the expenses were too much. For days, I cried and blamed myself. The betrayal, the disappointment and my mom's health issues all of this stress made me want to give up on life. But one day, I decided that sitting in pain wouldn’t solve anything. I picked myself up and chose to fight for what I lost then I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how he helped people recover their funds from online fraud. I emailed all the transactions and paperwork I had with the fraudulent organization and they helped me recover all my lost money in just five days. If you have ever fallen victim to scammers, contact GREAT WHIP RECOVERY CYBER SERVICES to help you recover every penny you have lost. (Text +1(406)2729101) Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site (Email [email protected])
19.11.25 16:30 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
19.11.25 16:30 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
20.11.25 15:55 mariotuttle94

HIRE THE BEST HACKER ONLINE FOR CRYPTO BITCOIN SCAM RECOVERY / iFORCE HACKER RECOVERY After a security breach, my husband lost $133,000 in Bitcoin. We sought help from a professional cybersecurity team iForce Hacker Recovery they guided us through each step of the recovery process. Their expertise allowed them to trace the compromised funds and help us understand how the breach occurred. The experience brought us clarity, restored a sense of stability, and reminded us of the importance of strong digital asset and security practices. Website: ht tps:/ /iforcehackers. c om WhatsApp: +1 240-803-3706 Email: iforcehk @ consultant. c om
21.11.25 10:56 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: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
21.11.25 10:56 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: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
22.11.25 04:41 VERONICAFREDDIE809

Earlier this year, I made a mistake that changed everything. I downloaded what I thought was a legitimate trading app I’d found through a Telegram channel. At first, everything looked real until I tried to withdraw. My entire investment vanished into a bot account, and that’s when the truth hit me: I had been scammed. I can’t describe the feeling. It was as if the ground dropped out from under me. I blamed myself. I felt stupid, ashamed, helpless every painful emotion at once. For a while, I couldn’t even talk about it. I thought no one would understand. But then I got connected to the best female expert AGENT Jasmine Lopez,,( [email protected] ) ,She didn’t brush me off or judge me. She took my fear seriously. She followed leads I didn’t even know existed, and identified multiple off-chain indicators and wallet clusters linked to the scammer network, she helped me understand what had truly happened behind the scenes. For the first time since everything fell apart, I felt hope. Hearing that other people students, parents, hardworking people had been targeted the same way made me realize I wasn’t alone. What happened to us wasn’t stupidity. It was a coordinated attack. We were prey in a system built to deceive. And somehow, through all the chaos, Agent Jasmine stepped in and shined a light into the darkest moment of my life. I’m still healing from the experience. It changed me. But it also reminded me that even when you think you’re at the end, sometimes a lifeline appears where you least expect it. Contact her at [email protected] WhatsApp at +44 736-644-5035.
22.11.25 22:04 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
22.11.25 22:04 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
22.11.25 22:05 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
23.11.25 03:34 Matt Kegan

SolidBlock Forensics are absolutely the best Crypto forensics team, they're swift to action and accurate
23.11.25 09:54 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
23.11.25 18:01 mosbygerry

I recently had the opportunity to work with a skilled programmer who specialized in recovering crypto assets, and the results were nothing short of impressive. The experience not only helped me regain control of my investments but also provided valuable insight into the intricacies of cryptocurrency technology and cybersecurity. The journey began when I attempted to withdraw $183,000 from an investment firm, only to encounter a series of challenges that made it impossible for me to access my funds. Despite seeking assistance from individuals claiming to be Bitcoin miners, I was unable to recover my investments. The situation was further complicated by the fact that all my deposits were made using various cryptocurrencies that are difficult to trace. However, I persisted in my pursuit of recovery, driven by the determination to reclaim my losses. It was during this time that I discovered TechY Force Cyber Retrieval, a team of experts with a proven track record of successfully recovering crypto assets. With their assistance, I was finally able to recover my investments, and in doing so, gained a deeper understanding of the complex mechanisms that underpin cryptocurrency transactions. The experience taught me that with the right expertise and guidance, even the most seemingly insurmountable challenges can be overcome. I feel a sense of obligation to share my positive experience with others who may have fallen victim to cryptocurrency scams or are struggling to recover their investments. If you find yourself in a similar situation, I highly recommend seeking the assistance of a trustworthy and skilled programmer, such as those at TechY Force Cyber Retrieval. WhatsApp (+1561726 3697) or (+1561726 3697). Their expertise and dedication to helping individuals recover their crypto assets are truly commendable, and I have no hesitation in endorsing their services to anyone in need. By sharing my story, I hope to provide a beacon of hope for those who may have lost faith in their ability to recover their investments and to emphasize the importance of seeking professional help when navigating the complex world of cryptocurrency.
24.11.25 11:43 michaeldavenport238

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
24.11.25 11:43 michaeldavenport238

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
24.11.25 16:34 Mundo

I wired 120k in crypto to the wrong wallet. One dumb slip-up, and poof gone. That hit me hard. Lost everything I had built up. Crypto moves on the blockchain. It's like a public record book. Once you send, that's it. No take-backs. Banks can fix wire mistakes. Not here. Transfers stick forever. a buddy tipped me off right away. Meet Sylvester Bryant. Guy's a pro at pulling back lost crypto. Handles cases others can't touch, he spots scammer moves cold. Follows money down secret paths. Mixers. Fake trades. Hidden swaps. You name it, he tracks it. this happens to tons of folks. Fat-finger a key. Miss one digit in the address. Boom. Billions vanish like that each year. I panicked. Figured my stash was toast for good. Bryant flipped the script. He jumps on hard jobs quick. Digs deep. Cracks the trail. Got my funds back safe. You're in the same boat? Don't sit there. Hit him up today. Email [email protected]. WhatsApp +1 512 577 7957. Or +44 7428 662701. Time's your enemy here. Scammers spend fast. Chains churn non-stop. Move now. Grab your cash back home.
25.11.25 05:15 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
25.11.25 13:31 mickaelroques52

CRYPTO TRACING AND INVESTIGATION EXPERT: HOW TO RECOVER STOLEN CRYPTO_HIRE RAPID DIGITAL RECOVERY
25.11.25 13:31 mickaelroques52

I’ve always considered myself a careful person when it comes to money, but even the most cautious people can be fooled. A few months ago, I invested some of my Bitcoin into what I believed was a legitimate platform. Everything seemed right, professional website, live chat support and even convincing testimonials. I thought I had done my homework. But when I tried to withdraw my funds, everything fell apart. My account was blocked, the so-called support team disappeared and I realized I had been scammed. The shock was overwhelming. I couldn’t believe I had fallen for it. That Bitcoin represented years of savings and sacrifices and it felt like everything had been stolen from me in seconds. I didn’t sleep for days and I was angry at myself for trusting the wrong people. In my desperation, I started searching for solutions and came across Rapid Digital Recovery. At first, I thought it was just another promise that would lead nowhere. But after speaking with them, I realized this was different. They were professional, clear and understanding. They explained exactly how they track stolen funds through blockchain forensics and what steps would be taken in my case. I gave them all the transaction details and they immediately got to work. What impressed me most was their transparency, they gave me updates regularly and kept me involved in the process. After weeks of investigation, they achieved what I thought was impossible: they recovered my stolen Bitcoin and safely returned it to my wallet. The relief I felt that day is indescribable. I went from feeling hopeless and broken to feeling like I had been given a second chance. I am forever grateful to Rapid Digital Recovery. They didn’t just recover my money, they restored my peace of mind. If you’re reading this because you’ve been scammed, please know you’re not alone and that recovery is possible. I’m living proof that with the right help, you can get your funds back... Contact Info Below WhatSapp: + 1 414 807 1485 Email: rapiddigitalrecovery (@) execs. com Telegram: + 1 680 5881 631
26.11.25 18:18 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.11.25 18:20 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.11.25 19:13 James Robert

I am James Robert from Chicago. Few months ago, I fell victim to an online Bitcoin investment scheme that promised high returns within a short period. At first, everything seemed legitimate, their website looked professional, and the people behind it were very convincing. I invested a significant amount of money about $440,000 with the way they talk to me into investing on their bitcoin platform. Two months later I realized that it was a scam when I could no longer have access to my account and couldn’t withdraw my money. At first, I lost hope that I wouldn't be able to get my money back, I cried and was angry at how I even fell victim to a scam. For days after doing some research and seeking professional help online, I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how they have helped people recover their money back from scammers. I reported the case immediately to them and gather every transaction detail, documentation and sent it to them. Today, I’m very happy because the GREAT WHIP RECOVERY CYBER SERVICES help me recover all my money I was scammed. You can contact GREAT WHIP RECOVERY CYBER SERVICES if you have ever fallen victim to scam. Email: [email protected] or Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site
26.11.25 19:13 James Robert

I am James Robert from Chicago. Few months ago, I fell victim to an online Bitcoin investment scheme that promised high returns within a short period. At first, everything seemed legitimate, their website looked professional, and the people behind it were very convincing. I invested a significant amount of money about $440,000 with the way they talk to me into investing on their bitcoin platform. Two months later I realized that it was a scam when I could no longer have access to my account and couldn’t withdraw my money. At first, I lost hope that I wouldn't be able to get my money back, I cried and was angry at how I even fell victim to a scam. For days after doing some research and seeking professional help online, I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how they have helped people recover their money back from scammers. I reported the case immediately to them and gather every transaction detail, documentation and sent it to them. Today, I’m very happy because the GREAT WHIP RECOVERY CYBER SERVICES help me recover all my money I was scammed. You can contact GREAT WHIP RECOVERY CYBER SERVICES if you have ever fallen victim to scam. Email: [email protected] or Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site
26.11.25 19:13 James Robert

I am James Robert from Chicago. Few months ago, I fell victim to an online Bitcoin investment scheme that promised high returns within a short period. At first, everything seemed legitimate, their website looked professional, and the people behind it were very convincing. I invested a significant amount of money about $440,000 with the way they talk to me into investing on their bitcoin platform. Two months later I realized that it was a scam when I could no longer have access to my account and couldn’t withdraw my money. At first, I lost hope that I wouldn't be able to get my money back, I cried and was angry at how I even fell victim to a scam. For days after doing some research and seeking professional help online, I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how they have helped people recover their money back from scammers. I reported the case immediately to them and gather every transaction detail, documentation and sent it to them. Today, I’m very happy because the GREAT WHIP RECOVERY CYBER SERVICES help me recover all my money I was scammed. You can contact GREAT WHIP RECOVERY CYBER SERVICES if you have ever fallen victim to scam. Email: [email protected] or Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site
27.11.25 10:56 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.11.25 10:56 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.11.25 20:04 deborah113

Scammed Crypto Asset Recovery Solution Hire iFORCE HACKER RECOVERY When I traded online, I lost both my investment money and the anticipated gains. Before permitting any withdrawals, the site kept requesting more money, and soon I recognized I had been duped. It was really hard to deal with the loss after their customer service ceased responding. I saw a Facebook testimonial about how iForce Hacker Recovery assisted a victim of fraud in getting back the bitcoin she had transferred to con artists. I contacted iForce Hacker Recovery, submitted all relevant case paperwork, and meticulously followed the guidelines. I'm relieved that I was eventually able to get my money back, including the gains that were initially displayed on my account. I'm sharing my story to let others who have been conned know that you can recover your money. WhatsApp: +1 240-803-3706 Email: iforcehk @ consultant. c om Website: ht tps:/ /iforcehackers. c om
27.11.25 23:48 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.11.25 23:48 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.11.25 00:08 VERONICAFREDDIE809

Earlier this year, I made a mistake that changed everything. I downloaded what I thought was a legitimate trading app I’d found through a Telegram channel. At first, everything looked real until I tried to withdraw. My entire investment vanished into a bot account, and that’s when the truth hit me: I had been scammed. I can’t describe the feeling. It was as if the ground dropped out from under me. I blamed myself. I felt stupid, ashamed, helpless every painful emotion at once. For a while, I couldn’t even talk about it. I thought no one would understand. But then I found someone Agent Jasmine Lopez ([email protected])WhatsApp at +44 736-644-5035. ,She didn’t brush me off or judge me. She took my fear seriously. She followed leads I didn’t even know existed, and identified multiple off-chain indicators and wallet clusters linked to the scammer network, she helped me understand what had truly happened behind the scenes. For the first time since everything fell apart, I felt hope. Hearing that other people students, parents, hardworking people had been targeted the same way made me realize I wasn’t alone. What happened to us wasn’t stupidity. It was a coordinated attack. We were prey in a system built to deceive. And somehow, through all the chaos, Agent Jasmine stepped in and shined a light into the darkest moment of my life. I’m still healing from the experience. It changed me. But it also reminded me that even when you think you’re at the end, sometimes a lifeline appears where you least expect it.
28.11.25 11:15 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
28.11.25 11:15 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
28.11.25 11:43 elizabethmadison

My name is Elizabeth Madison currently living in New York. There was a time I felt completely broken. I had trusted a fraudulent bitcoin investment organization, who turned out to be a fraudster. I sent money, believing their sweet words and promises on the interest rate I will get back in return, only to realize later that I’ve been scammed. On the day of withdrawal there was no money in my account. The pain hit deep. I couldn’t sleep, I kept asking myself how I could have been so careless, meanwhile my mom was battling with a stroke and the expenses were too much. For days, I cried and blamed myself. The betrayal, the disappointment and my mom's health issues all of this stress made me want to give up on life. But one day, I decided that sitting in pain wouldn’t solve anything. I picked myself up and chose to fight for what I lost then I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how he helped people recover their funds from online fraud. I emailed all the transactions and paperwork I had with the fraudulent organization and they helped me recover all my lost money in just five days. If you have ever fallen victim to scammers, contact GREAT WHIP RECOVERY CYBER SERVICES to help you recover every penny you have lost. (Text +1(406)2729101) Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site (Email [email protected])
28.11.25 11:43 elizabethmadison

My name is Elizabeth Madison currently living in New York. There was a time I felt completely broken. I had trusted a fraudulent bitcoin investment organization, who turned out to be a fraudster. I sent money, believing their sweet words and promises on the interest rate I will get back in return, only to realize later that I’ve been scammed. On the day of withdrawal there was no money in my account. The pain hit deep. I couldn’t sleep, I kept asking myself how I could have been so careless, meanwhile my mom was battling with a stroke and the expenses were too much. For days, I cried and blamed myself. The betrayal, the disappointment and my mom's health issues all of this stress made me want to give up on life. But one day, I decided that sitting in pain wouldn’t solve anything. I picked myself up and chose to fight for what I lost then I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how he helped people recover their funds from online fraud. I emailed all the transactions and paperwork I had with the fraudulent organization and they helped me recover all my lost money in just five days. If you have ever fallen victim to scammers, contact GREAT WHIP RECOVERY CYBER SERVICES to help you recover every penny you have lost. (Text +1(406)2729101) Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site (Email [email protected])
29.11.25 12:35 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.11.25 12:35 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.11.25 12:35 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
30.11.25 20:37 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
01.12.25 12:27 Thomas Muller

YOU CAN REACH OUT TO GREAT WHIP RECOVERY CYBER SERVICES FOR HELP TO RECOVER YOUR STOLEN BTC OR ETH BACK WHATSAPP +1(208)713-0697 I once fell victim to online investment scheme that cost me a devastating €254,000. I’m Thomas Muller from Berlin, Germany. The person I trusted turned out to be a fraud, and the moment I realized I’d been deceived, my entire world stopped. I immediately began searching for legitimate ways to recover my funds and hold the scammer accountable. During my search, I came across several testimonies of how Great Whip Recovery Cyber Services helped some people recover money they lost to cyber fraud, I contacted Great Whip Recovery Cyber Service team and provided all the evidence I had. Within about 36 hours, the experts traced the digital trail left by the fraudster, the individual was eventually tracked down and I recovered all my money back. You can contact them with, website https://greatwhiprecoveryc.wixsite.com/greatwhip-site text +1(406)2729101 email [email protected]
01.12.25 12:27 Thomas Muller

YOU CAN REACH OUT TO GREAT WHIP RECOVERY CYBER SERVICES FOR HELP TO RECOVER YOUR STOLEN BTC OR ETH BACK WHATSAPP +1(208)713-0697 I once fell victim to online investment scheme that cost me a devastating €254,000. I’m Thomas Muller from Berlin, Germany. The person I trusted turned out to be a fraud, and the moment I realized I’d been deceived, my entire world stopped. I immediately began searching for legitimate ways to recover my funds and hold the scammer accountable. During my search, I came across several testimonies of how Great Whip Recovery Cyber Services helped some people recover money they lost to cyber fraud, I contacted Great Whip Recovery Cyber Service team and provided all the evidence I had. Within about 36 hours, the experts traced the digital trail left by the fraudster, the individual was eventually tracked down and I recovered all my money back. You can contact them with, website https://greatwhiprecoveryc.wixsite.com/greatwhip-site text +1(406)2729101 email [email protected]
01.12.25 23:45 michaeldavenport238

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
01.12.25 23:45 michaeldavenport238

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
02.12.25 02:21 donald121

In 2025 alone, hackers stole over $1.5 billion in digital assets from users worldwide. That's a wake-up call for anyone holding crypto. Theft hits hard because once funds move, they're tough to get back. Common ways it happens include phishing emails that trick you into giving up keys, big exchange breaches, or malware sneaking into your wallet. Marie guide walks you through steps to recover stolen cryptocurrency. You'll learn quick actions to stop more loss, how to trace funds, and ways to fight back legally. Plus, tips to avoid this mess next time. reach her (infocyberrecoveryinc@gmail com and whatsapp:+1 7127594675)
02.12.25 15:05 Matt Kegan

Reach out to SolidBlock Forensics if you want to get back your coins from fake crypto investment or your wallet was compromised and all your coins gone. SolidBlock Forensics provide deep ethical analysis and investigation that enables them to trace these schemes, and recover all your funds. Their services are professional and reliable.
03.12.25 09:22 tyrelldavis1

I still recall the day I fell victim to an online scam, losing a substantial amount of money to a cunning fraudster. The feeling of helplessness and despair that followed was overwhelming, and I thought I had lost all hope of ever recovering my stolen funds. However, after months of searching for a solution, I stumbled upon a beacon of hope - GRAYWARE TECH SERVICE, a highly reputable and exceptionally skilled investigative and recovery firm. Their team of expert cybersecurity professionals specializes in tracking and retrieving money lost to internet fraud, and I was impressed by their unwavering dedication to helping victims like me. With their extensive knowledge and cutting-edge technology, they were able to navigate the complex world of online finance and identify the culprits behind my loss. What struck me most about GRAYWARE TECH SERVICE was their unparalleled expertise and exceptional customer service. They took the time to understand my situation, provided me with regular updates, and kept me informed throughout the entire recovery process. Their transparency and professionalism were truly reassuring, and I felt confident that I had finally found a reliable partner to help me recover my stolen money. Thanks to GRAYWARE TECH SERVICE, I was able to recover a significant portion of my lost funds, and I am forever grateful for their assistance. Their success in retrieving my money not only restored my financial stability but also restored my faith in the ability of authorities to combat online fraud. If you have fallen victim to internet scams, I highly recommend reaching out to GRAYWARE TECH SERVICE - their expertise and dedication to recovering stolen funds are unparalleled, and they may be your only hope for retrieving what is rightfully yours. You can reach them on whatsapp+18582759508 web at ( https://graywaretechservice.com/ ) also on Mail: ([email protected]
03.12.25 21:01 VERONICAFREDDIE809

Earlier this year, I made a mistake that changed everything. I downloaded what I thought was a legitimate trading app I’d found through a Telegram channel. At first, everything looked real until I tried to withdraw. My entire investment vanished into a bot account, and that’s when the truth hit me: I had been scammed. I can’t describe the feeling. It was as if the ground dropped out from under me. I blamed myself. I felt stupid, ashamed, helpless every painful emotion at once. For a while, I couldn’t even talk about it. I thought no one would understand. But then I found someone Agent Jasmine Lopez ([email protected]) ,She didn’t brush me off or judge me. She took my fear seriously. She followed leads I didn’t even know existed, and identified multiple off-chain indicators and wallet clusters linked to the scammer network, she helped me understand what had truly happened behind the scenes. For the first time since everything fell apart, I felt hope. Hearing that other people students, parents, hardworking people had been targeted the same way made me realize I wasn’t alone. What happened to us wasn’t stupidity. It was a coordinated attack. We were prey in a system built to deceive. And somehow, through all the chaos, Agent Jasmine stepped in and shined a light into the darkest moment of my life. I’m still healing from the experience. It changed me. But it also reminded me that even when you think you’re at the end, sometimes a lifeline appears where you least expect it. Contact her at [email protected] WhatsApp at +44 736-644-5035.
03.12.25 22:17 Tonerdomark

I lost $300,000 in USDC to a phishing scam. Scammers tricked me with a fake wallet link. They drained my account fast. I felt hopeless. No way to get it back. Then Sylvester stepped in. His skills traced the funds. He recovered every bit. USDC is a stablecoin tied to the dollar. Phishing scams hit hard in crypto. They fool you with urgent emails or sites. Billions vanish each year this way. Sylvester knows blockchain tracks. He used tools to follow the trail. I got my money back in weeks. Skills like his turn loss to win. Don't wait if scammed. Contact Mr. Sylvester now. Email: yt7cracker@gmail. com. WhatsApp only: + 1 512 577 7957 or + 44 7428 662701. He helped me. He can help you.
04.12.25 01:37 michaeldavenport238

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
04.12.25 01:37 michaeldavenport238

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
04.12.25 04:35 Tonerdomark

I lost $300,000 in USDC to a phishing scam. Scammers tricked me with a fake wallet link. They drained my account fast. I felt hopeless. No way to get it back. Then Sylvester stepped in. His skills traced the funds. He recovered every bit. USDC is a stablecoin tied to the dollar. Phishing scams hit hard in crypto. They fool you with urgent emails or sites. Billions vanish each year this way. Sylvester knows blockchain tracks. He used tools to follow the trail. I got my money back in weeks. Skills like his turn loss to win. Don't wait if scammed. Contact Mr. Sylvester now. Email: [email protected]. WhatsApp only: + 1 512 577 7957 or + 44 7428 662701. He helped me. He can help you.
04.12.25 10:32 Tonerdomark

I lost $300,000 in USDC to a phishing scam. Scammers tricked me with a fake wallet link. They drained my account fast. I felt hopeless. No way to get it back. Then Sylvester stepped in. His skills traced the funds. He recovered every bit. USDC is a stablecoin tied to the dollar. Phishing scams hit hard in crypto. They fool you with urgent emails or sites. Billions vanish each year this way. Sylvester knows blockchain tracks. He used tools to follow the trail. I got my money back in weeks. Skills like his turn loss to win. Don't wait if scammed. Contact Mr. Sylvester now. Email: [email protected]. WhatsApp only: + 1 512 577 7957 or + 44 7428 662701. He helped me. He can help you.
04.12.25 18:25 smithhazael

Hire Proficient Expert Consultant For any form of lost crypto "A man in Indonesia tragically took his own life after losing his family's savings to a scam. The shame and blame were too much to bear. It's heartbreaking to think he might still be alive if he knew help existed. "PROFICIENT EXPERT CONSULTANTS, I worked alongside PROFICIENT EXPERT CONSULTANTS when I lost my funds to an investment platform on Telegram. PROFICIENT EXPERT CONSULTANTS did a praiseworthy job, tracked and successfully recovered all my lost funds a total of $770,000 within 48hours after contacting them, with their verse experience in recovery issues and top tier skills they were able to transfer back all my funds into my account, to top it up I had full access to my account and immediately converted it to cash, they handled my case with professionalism and empathy and successfully recovered all my lost funds, with so many good reviews about PROFICIENT EXPERT CONSULTANTS, I’m glad I followed my instincts after reading all the reviews and I was able to recovery everything I thought I had lost, don’t commit suicide if in any case you are caught in the same situation, contact: Proficientexpert@consultant. com Telegram: @ PROFICIENTEXPERT, the reliable experts in recovery.
04.12.25 21:45 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
04.12.25 21:45 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
05.12.25 08:35 into11

The digital world of cryptocurrency offers big chances, but it also hides tricky scams. Losing your crypto to fraud feels awful. It can leave you feeling lost and violated. This guide tells you what to do right away if a crypto scam has hit you. These steps can help you get funds back or stop more trouble. Knowing what to do fast can change everything,reach marie ([email protected] and whatsapp:+1 7127594675)
05.12.25 08:48 Tonerdomark

SYLVESTER BRYANT WAS A PROFESSIONAL/ RELIABLE HACKER AND HIGHLY RECOMMENDED I’m very excited to speak about him as a Bitcoin Recovery agent, this cyber security company was able to assist me in recovering my stolen funds in cryptocurrency. I’m truly amazed by their excellent service and professional work. I never thought I could get back my funds until I approached them with my problems and provided all the necessary information. It took them time to recover my funds and I was amazed. Without any doubt, I highly recommend Sylvester for your BITCOIN, USDC, USDT, ETH Recovery, for all Cryptocurrency recovery, digital funds recovery, hacking Related issues, contact Sylvester Bryant professional services waapp only= +1 512 577 7957 or + 44 7428 662701 EMAIL = [email protected]
06.12.25 01:44 Tonerdomark

SYLVESTER BRYANT WAS A PROFESSIONAL/ RELIABLE HACKER AND HIGHLY RECOMMENDED I’m very excited to speak about him as a Bitcoin Recovery agent, this cyber security company was able to assist me in recovering my stolen funds in cryptocurrency. I’m truly amazed by their excellent service and professional work. I never thought I could get back my funds until I approached them with my problems and provided all the necessary information. It took them time to recover my funds and I was amazed. Without any doubt, I highly recommend Sylvester for your BITCOIN, USDC, USDT, ETH Recovery, for all Cryptocurrency recovery, digital funds recovery, hacking Related issues, contact Sylvester Bryant professional services waapp only= +1 512 577 7957 or + 44 7428 662701 EMAIL = [email protected]
06.12.25 01:48 Tonerdomark

SYLVESTER BRYANT WAS A PROFESSIONAL/ RELIABLE HACKER AND HIGHLY RECOMMENDED I’m very excited to speak about him as a Bitcoin Recovery agent, this cyber security company was able to assist me in recovering my stolen funds in cryptocurrency. I’m truly amazed by their excellent service and professional work. I never thought I could get back my funds until I approached them with my problems and provided all the necessary information. It took them time to recover my funds and I was amazed. Without any doubt, I highly recommend Sylvester for your BITCOIN, USDC, USDT, ETH Recovery, for all Cryptocurrency recovery, digital funds recovery, hacking Related issues, contact Sylvester Bryant professional services waapp only= +1 512 577 7957 or + 44 7428 662701 EMAIL = [email protected]
06.12.25 10:36 Thomas Muller

YOU CAN REACH OUT TO GREAT WHIP RECOVERY CYBER SERVICES FOR HELP TO RECOVER YOUR STOLEN BTC OR ETH BACK WHATSAPP +1(208)713-0697 I once fell victim to online investment scheme that cost me a devastating €254,000. I’m Thomas Muller from Berlin, Germany. The person I trusted turned out to be a fraud, and the moment I realized I’d been deceived, my entire world stopped. I immediately began searching for legitimate ways to recover my funds and hold the scammer accountable. During my search, I came across several testimonies of how Great Whip Recovery Cyber Services helped some people recover money they lost to cyber fraud, I contacted Great Whip Recovery Cyber Service team and provided all the evidence I had. Within about 36 hours, the experts traced the digital trail left by the fraudster, the individual was eventually tracked down and I recovered all my money back. You can contact them with, website https://greatwhiprecoveryc.wixsite.com/greatwhip-site text +1(406)2729101 email [email protected]
06.12.25 10:36 Thomas Muller

YOU CAN REACH OUT TO GREAT WHIP RECOVERY CYBER SERVICES FOR HELP TO RECOVER YOUR STOLEN BTC OR ETH BACK WHATSAPP +1(208)713-0697 I once fell victim to online investment scheme that cost me a devastating €254,000. I’m Thomas Muller from Berlin, Germany. The person I trusted turned out to be a fraud, and the moment I realized I’d been deceived, my entire world stopped. I immediately began searching for legitimate ways to recover my funds and hold the scammer accountable. During my search, I came across several testimonies of how Great Whip Recovery Cyber Services helped some people recover money they lost to cyber fraud, I contacted Great Whip Recovery Cyber Service team and provided all the evidence I had. Within about 36 hours, the experts traced the digital trail left by the fraudster, the individual was eventually tracked down and I recovered all my money back. You can contact them with, website https://greatwhiprecoveryc.wixsite.com/greatwhip-site text +1(406)2729101 email [email protected]
06.12.25 10:39 michaeldavenport238

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06.12.25 10:42 michaeldavenport238

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07.12.25 08:43 Tonerdomark

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08.12.25 02:17 liam

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08.12.25 09:07 Tonerdomark

SYLVESTER BRYANT WAS A PROFESSIONAL/ RELIABLE HACKER AND HIGHLY RECOMMENDED I’m very excited to speak about him as a Bitcoin Recovery agent, this cyber security company was able to assist me in recovering my stolen funds in cryptocurrency. I’m truly amazed by their excellent service and professional work. I never thought I could get back my funds until I approached them with my problems and provided all the necessary information. It took them time to recover my funds and I was amazed. Without any doubt, I highly recommend Sylvester for your BITCOIN, USDC, USDT, ETH Recovery, for all Cryptocurrency recovery, digital funds recovery, hacking Related issues, contact Sylvester Bryant professional services waapp only= +1 512 577 7957 or + 44 7428 662701 EMAIL = [email protected]
09.12.25 00:18 swanky

For a long time, I had heard tales of individuals striking it rich through cryptocurrency investments, but I had little knowledge of how the system operated. The potential for financial gain piqued my interest, and I decided to dive in and invest. To help me navigate this complex landscape, I joined a group of online traders who promised to guide me through the investment process. Their confidence and expertise made me feel reassured about my decision.After spending some time learning from them and observing their trading strategies, I felt compelled to invest a substantial amount of money to which i lost, now in search of recovering my funds i got referred to anthonydavies on telegram a funds recovery specialist with his team help i was able to get back $300000 of my usdc back. you can reach him via anthonydaviestech AT gmail dot com
09.12.25 01:01 Tonerdomark

SYLVESTER BRYANT WAS A PROFESSIONAL/ RELIABLE HACKER AND HIGHLY RECOMMENDED I’m very excited to speak about him as a Bitcoin Recovery agent, this cyber security company was able to assist me in recovering my stolen funds in cryptocurrency. I’m truly amazed by their excellent service and professional work. I never thought I could get back my funds until I approached them with my problems and provided all the necessary information. It took them time to recover my funds and I was amazed. Without any doubt, I highly recommend Sylvester for your BITCOIN, USDC, USDT, ETH Recovery, for all Cryptocurrency recovery, digital funds recovery, hacking Related issues, contact Sylvester Bryant professional services waapp only= +1 512 577 7957 or + 44 7428 662701 EMAIL = Yt7CRACKER@gmail. com
09.12.25 05:44 swanky

For a long time, I had heard tales of individuals striking it rich through cryptocurrency investments, but I had little knowledge of how the system operated. The potential for financial gain piqued my interest, and I decided to dive in and invest. To help me navigate this complex landscape, I joined a group of online traders who promised to guide me through the investment process. Their confidence and expertise made me feel reassured about my decision.After spending some time learning from them and observing their trading strategies, I felt compelled to invest a substantial amount of money to which i lost, now in search of recovering my funds i got referred to anthonydavies on telegram a funds recovery specialist with his team help i was able to get back $300000 of my usdc back. you can reach him via anthonydaviestech AT gmail dot com
09.12.25 10:24 lane3215

It is distressing to lose USDT to a bitcoin wallet hack. Although challenging, recovering stolen USDT is feasible. Your chances increase if you move swiftly and strategically. Marie can help you with reporting the theft, recovering USDT, and taking immediate action. You can reach her via mail at [email protected], WhatsApp at +1 7127594675.
09.12.25 10:25 lane3215

It is distressing to lose USDT to a bitcoin wallet hack. Although challenging, recovering stolen USDT is feasible. Your chances increase if you move swiftly and strategically. Marie can help you with reporting the theft, recovering USDT, and taking immediate action. You can reach her via mail at [email protected], WhatsApp at +1 7127594675.
09.12.25 14:16 Matt Kegan

Grateful i came across SolidBlock Forensics. After investing in crypto trade and couldn't make withdrawals, it dawned on me something was wrong. They kept on asking for taxes, fees for maintenance, and more money for admin reasons. But being represented by SolidBlock Forensics, i was able to file reports, and finally, received all my investments with returns. Its great to know we have professionals that handle such issues and get the job done.