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Главное по ML/DL, часть 2: Вопрос → Краткий ответ → Разбор → Пример кода. SVD/PCA. Bias-variance. Деревья. Бустинг

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. Поэтому попробуйте сами решить предложенную задачку и придумать свою!

Будет здорово получить ваши задачи и в следующих выпусках разобрать!

Мы продолжаем. Обязательно испытайте себя в предыдущей [1] части!

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

11. Анализ главных компонент. Связь с SVD. Теорема Эккарта-Янга. Как применять PCA на практике.

📌 Краткий ответ

PCA (Principal Component Analysis или анализ главных компонент) — метод понижения размерности, который:

Решает задачу апроксимации исходной матрицы, матрицами меньшего ранга (как например ALS)
Ее можно решать как задачу оптимизации функции ошибки MSE или конструктивно с SVD
Еще одна итерпретация - предсказание исходной матрицы скалярным произведением латентных векторов юзера и товара

Ищет такие оси (направления), вдоль которых данные имеют максимальную дисперсию
Проецирует данные на первые таких осей (компонент), сохраняя как можно больше информации (в смысле дисперсии) - почему? идем к SVD

Реализуется через SVD (Singular value decomposition или сингулярное разложение) - разложение матрицы на две ортонормированные [поворот] и диагональную [растяжение] (с сингулярными числами=важность/дисперсия нового признака)

Строки у разжатия можно перемещать (соответвенно, что финальная матрица не изменится) $\Rightarrow$ можно оставить только самые важные признаки!

Теорема Эккарта-Янга - утверждает, такая апроксимация внутри своего ранга по норме Фробениуса наименьшая!

🔬 Подробный разбор

На одном дыхании можно послушать тут или почитать хендбук. Отличный английский видеоформат .

💻 Сжимаем картинку через SVD и смотрим на важность направлений

Научимся представлять картинку меньшим кол-вом памяти с помощью SVD !

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_sample_image
from skimage.color import rgb2gray
from skimage.transform import resize

# --- Загружаем и обрабатываем картинку
china = load_sample_image("china.jpg")   # встроенное изображение
gray = rgb2gray(china)                   # перевод в ч/б
gray = resize(gray, (256, 256), anti_aliasing=True)  # уменьшаем до квадрата

# --- SVD
U, S, VT = np.linalg.svd(gray, full_matrices=False)

# --- Восстановление при разных k
ks = [5, 20, 50, 100, 200]
fig, axes = plt.subplots(1, len(ks) + 1, figsize=(15, 4))

# Оригинал
axes[0].imshow(gray, cmap='gray')
axes[0].set_title("Оригинал")
axes[0].axis('off')

# При разных k
for i, k in enumerate(ks):
    approx = U[:, :k] @ np.diag(S[:k]) @ VT[:k, :]
    axes[i + 1].imshow(approx, cmap='gray')
    axes[i + 1].set_title(f"k = {k}")
    axes[i + 1].axis('off')

plt.suptitle("Сжатие изображения с помощью SVD")
plt.tight_layout()
plt.show()

# Расчёт накопленной доли дисперсии
explained = np.cumsum(S) / np.sum(S)

# Отрисовка: сингулярные числа + накопленная доля
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))

# --- 1. Сами сингулярные числа (в лог масштабе)
ax1.plot(S, marker='o')
ax1.set_yscale("log")
ax1.set_title("Сингулярные значения")
ax1.set_xlabel("Номер компоненты")
ax1.set_ylabel("Значение (log)")
ax1.grid(True)

# --- 2. Накопленная доля дисперсии
ax2.plot(explained, label='Cуммарная доля дисперсии')
ax2.axhline(0.9, color='red', linestyle='--', label='90% информации')
ax2.set_xlabel("Число компонент")
ax2.set_ylabel("Накопленная доля")
ax2.set_title("Сколько информации несут сингулярные значения")
ax2.grid(True)
ax2.legend()

plt.tight_layout()
plt.show()

💻 Проецируем многомерные данные (картинки цифр) в 2D с помощью PCA

Визуализируем датасет рукописных цифр (digits) — в нём 64 признака (8×8 картинка), и сожмём до 2 главных компонент, чтобы посмотреть, как PCA группирует похожие объекты:

from sklearn.datasets import load_digits
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt

# --- Загружаем данные
digits = load_digits()
X = digits.data       # 64 признака (8x8 пикселей)
y = digits.target     # метки (0-9)

# --- PCA до 2 компонент
pca = PCA(n_components=2)
X_pca = pca.fit_transform(X)

# --- Визуализация
plt.figure(figsize=(8, 6))
scatter = plt.scatter(X_pca[:, 0], X_pca[:, 1], c=y, cmap='tab10', s=15, alpha=0.8)
plt.legend(*scatter.legend_elements(), title="Цифры", loc="best", bbox_to_anchor=(1.05, 1))
plt.title("PCA-проекция данных (64D → 2D)")
plt.xlabel("1-я главная компонента")
plt.ylabel("2-я главная компонента")
plt.grid(True)
plt.tight_layout()
plt.show()

12. Этапы обучения, валидации и тестирования модели. Проблема переобучения, способы её обнаружения.

📌 Краткий ответ

Обучение ML-модели делится на три ключевых этапа:

Обучение (train) — модель подбирает параметры на обучающей выборке.
Валидация (validation) — подбираем гиперпараметры на валидационной выборке.
Тест (test) — финальная оценка качества, только один раз.

Бывают, что тест опускают и финальное качество берут лучшее с валидации, но это ведет к переобучению гиперпараметров.

Переобучение — это ситуация, когда модель слишком хорошо подгоняется под обучающую выборку, но плохо обобщает на новые данные.

Чтобы меньше зависеть от разбиение train/val/test используют обучение по фолдам (k-fold cross-validation) - Обучается моделей. Датасет делиться на частей, на k - 1 модель учиться, на оставшейся замеряется качество. Метрика усредняется.

Такой подход подход хоть устойчевее к шуму, но не всегда хочется делать бэггинг над этими моделей. Обычно в начале EDA (exploratory data analysis или разведочный анализ) проверяют, что разбиение train/val/test подходит и учат одну модель.

Как понять, что модель начала переобучаться? (если неграмотно сохранять чекпоинты, можно остаться с переобученной моделью!)

Метрика на train продолжает падать, а на val начала возрастать. (Если нету графиков, то метрика на train сильно лучше, чем на val)

Как бороться?

Early stopping (если метрика на валидации не уменьшалась k шагов - остановиться)
Регуляризации - /, Dropout/BatchNorm, аугментация данных и тд
Выбросить совсем незначащие признаки (если их очень много, модель будет на них отвлекаться, может и сойдется, но дОльше!)
Больше данных насыпать
Бэггинг (Bagging, от bootstrap aggregating) - учим несколько моделей на бутсреп данных и объединяем => уменьшаем дисперсию ответа

Классическая симптомы переобучения (можно раньше времени спутать с мифическим Double Descent)

🔬 Подробный разбор

Оказывается, не стоит раньше времени останавливать обучения, может быть у вас Double Descent. Ситуация в которой лосс на валидации взлетит, а потом начнет уменьшаться до меньших значений!

Я не знаю на практике у кого такое было. Но как явления очень интересное.

Подробнее про Double Descent можно почитать 1 и 2.

💻 Пример переобучения: наблюдаем за лоссом и предсказаниями

Смотрим, что происходит при увеличением эпох с лоссом и предсказаниями, если признаковое пространство недостаточно покрыто данными.

Я специалньо взял не очень много точек (=150), потому что данные достаточно очень легко устроены/разъединяются и при большем не наблюдается эффекта переобучения.

import torch
import torch.nn as nn
import torch.optim as optim
from sklearn.datasets import make_moons
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt
import numpy as np

# --- 1. Данные
X, y_true = make_moons(n_samples=150, noise=0.3, random_state=42)
# y_random = np.random.permutation(y_true)  # случайные метки!

# X_train, X_val, y_train, y_val = train_test_split(X, y_random, test_size=0.3, random_state=42)
X_train, X_val, y_train, y_val = train_test_split(X, y_true, test_size=0.3, random_state=42)

X_train_t = torch.tensor(X_train, dtype=torch.float32)
y_train_t = torch.tensor(y_train.reshape(-1, 1), dtype=torch.float32)

X_val_t = torch.tensor(X_val, dtype=torch.float32)
y_val_t = torch.tensor(y_val.reshape(-1, 1), dtype=torch.float32)

# --- 2. Модель
# h_size = 256
h_size = 100
model = nn.Sequential(
    nn.Linear(2, h_size),
    nn.ReLU(),
    nn.Linear(h_size, h_size),
    nn.ReLU(),
    nn.Linear(h_size, 1),
    nn.Sigmoid()
)

loss_fn = nn.BCELoss()
optimizer = optim.Adam(model.parameters(), lr=0.01)

train_losses, val_losses = [], []
snapshots = [0, 10, 30, 99]  # эпохи, для которых сохраним визуализацию

grids = np.meshgrid(
    np.linspace(X[:, 0].min() - 0.5, X[:, 0].max() + 0.5, 300),
    np.linspace(X[:, 1].min() - 0.5, X[:, 1].max() + 0.5, 300)
)
grid_points = np.c_[grids[0].ravel(), grids[1].ravel()]
grid_tensor = torch.tensor(grid_points, dtype=torch.float32)

# --- 3. Обучение
snapshots_preds = []

for epoch in range(100):
    model.train()
    y_pred = model(X_train_t)
    loss = loss_fn(y_pred, y_train_t)
    
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    model.eval()
    with torch.no_grad():
        val_pred = model(X_val_t)
        val_loss = loss_fn(val_pred, y_val_t)
        if epoch in snapshots:
            pred_grid = model(grid_tensor).reshape(300, 300)
            snapshots_preds.append((epoch, pred_grid.numpy()))
    
    train_losses.append(loss.item())
    val_losses.append(val_loss.item())

# --- 4. График потерь
plt.figure(figsize=(8, 5))
plt.plot(train_losses, label='Train Loss')
plt.plot(val_losses, label='Validation Loss')
plt.axvline(np.argmin(val_losses), linestyle='--', color='gray', label='Лучшая эпоха (val)')
plt.title("Переобучение: валидационная ошибка начинает расти")
plt.xlabel("Эпоха")
plt.ylabel("Binary CrossEntropy")
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

# --- 5. Визуализация данных + предсказания
fig, axes = plt.subplots(1, len(snapshots_preds), figsize=(16, 4))
for ax, (epoch, Z) in zip(axes, snapshots_preds):
    ax.contourf(grids[0], grids[1], Z, levels=20, cmap='coolwarm', alpha=0.7)
    ax.scatter(*X_train.T, c=y_train, cmap='bwr', s=15, edgecolor='k', label='Train')
    ax.scatter(*X_val.T, c=y_val, cmap='bwr', marker='x', s=15, label='Val')
    ax.set_title(f"Эпоха {epoch}")
    ax.axis('off')
plt.suptitle("Как модель обучается на шум: границы решений со временем")
plt.tight_layout()
plt.show()

💻 Переобучение полинома большой степени

# Повторный запуск после сброса состояния
import numpy as np
import matplotlib.pyplot as plt
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sklearn.pipeline import make_pipeline
from sklearn.metrics import mean_squared_error
from sklearn.model_selection import train_test_split

# --- 1. Генерируем данные
np.random.seed(42)
X = np.linspace(-3, 3, 10).reshape(-1, 1)  # мало точек
y = np.sin(X).ravel() + 0.3 * np.random.randn(*X.shape).ravel()

X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.3, random_state=42)

# --- 2. Обучаем модели с разной степенью полинома
degrees = [1, 4, 15]
preds = {}
val_errors = {}

x_plot = np.linspace(-3, 3, 300).reshape(-1, 1)

plt.figure(figsize=(15, 4))

for i, deg in enumerate(degrees):
    model = make_pipeline(PolynomialFeatures(degree=deg), LinearRegression())
    model.fit(X_train, y_train)
    
    y_plot = model.predict(x_plot)
    y_val_pred = model.predict(X_val)
    val_errors[deg] = mean_squared_error(y_val, y_val_pred)
    
    plt.subplot(1, 3, i + 1)
    plt.scatter(X_train, y_train, label='Train', color='blue')
    plt.scatter(X_val, y_val, label='Val', color='red', alpha=0.5)
    plt.plot(x_plot, y_plot, color='green', label=f"Poly deg={deg}")
    plt.title(f"deg={deg} | val MSE={val_errors[deg]:.2f}")
    plt.legend()
    plt.grid(True)

plt.suptitle("Сравнение моделей с разной степенью полинома")
plt.tight_layout()
plt.show()

val_errors
# {1: 0.0623793189026051, 4: 0.16693688909602888, 15: 714985.2317858242}

13. Стратегии валидации. Кросс-валидация. Утечки данных.

📌 Краткий ответ

Валидация — способ понять, как модель будет работать на новых данных и сравнить модели друг с другом.

Основные стратегии:

Hold-Out — просто делим на train/val.
K-Fold — учим моделей, валидируем по очереди на каждом фолде.
Stratified K-Fold — сохраняем пропорции классов.
TimeSeriesSplit — используем прошлое, предсказываем будущее.

Data leakage (утечка данных) — модель видит информацию, которую не должна:

Масштабирование или выбор признаков до train/val split
Использование target в признаках
Временная утечка

Обычно модель на своих данных показывает высокую метрику, а на продовых сильно хуже.

💻 Демонстрация val утечки в train. Предварительный отбор признаков SelectKBest на train VS train + val.

Удивительно, что даже с кроссвалидацией утечка сильно влияет на финальную метрику!

import numpy as np
from sklearn.datasets import make_classification
from sklearn.model_selection import cross_val_score
from sklearn.feature_selection import SelectKBest, f_classif
from sklearn.ensemble import RandomForestClassifier
from sklearn.pipeline import make_pipeline

# --- Данные: много признаков, немного информативных
X, y = make_classification(
    n_samples=1000, n_features=500, n_informative=30,
    random_state=42, shuffle=False
)

# --- ⚠️ Утечка: отбор признаков ДО cross-validation
selector = SelectKBest(score_func=f_classif, k=50)
X_leak = selector.fit_transform(X, y)

model = RandomForestClassifier(random_state=42)
scores_leak = cross_val_score(model, X_leak, y, cv=5)

# --- ✅ Честно: отбор фич ВНУТРИ кросс-валидации
pipeline = make_pipeline(
    SelectKBest(score_func=f_classif, k=50),
    RandomForestClassifier(random_state=42)
)
scores_clean = cross_val_score(pipeline, X, y, cv=5)

print(f"⚠️ CV accuracy с утечкой:  {scores_leak.mean():.3f}")
print(f"✅ CV accuracy без утечки: {scores_clean.mean():.3f}")

# ⚠️ CV accuracy с утечкой:  0.787
# ✅ CV accuracy без утечки: 0.754

14. Компромисс смещения-дисперсии (Bias-variance trade-off). Double Descent.

📌 Краткий ответ

Это разложение ошибки (и способ ее формально определить!) (на тестовой выборке) на три компоненты: bias, variance, noise (на нее не влияем). (Текущая формула верна для MSE, но аналоги существуют и для других!)

Показывает как выбрать оптимальную модель при некоторых предположениях: при усложнении модели bias падает, variance растет. Тогда сумма их графиков U-образная $\Rightarrow$ есть оптимум! (При Double Descent это не выполняется!)

Описание крайних ситуаций bias и variance

Теперь подробнее и по математически

Пусть:

$y(x, \varepsilon) = f(x) + \varepsilon$ — целевая переменная с шумом.

$\mathbb{E}[\varepsilon] = 0,\quad \mathrm{Var}[\varepsilon] = \mathbb{E}[\varepsilon^2] = \sigma^2$

— объект из тестовой выборки. - обучающая выборка
— алгоритм, обученный на случайной выборке ,

Тогда среднеквадратичная ошибка (MSE) алгоритма имеет вид:

$\mathbb{E}_x \mathbb{E}_{X, \varepsilon} \left[ y(x, \varepsilon) - a(x, X) \right]^2= \mathbb{E}_x \left( \underbrace{\left( \mathbb{E}_X[a(x, X)] - f(x) \right)^2}_{\text{смещение (bias)}^2}+ \underbrace{\text{Var}_X[a(x, X)]}_{\text{дисперсия (variance)}}+ \underbrace{\sigma^2}_{\text{шум}} \right)$

Пояснение:

$\text{bias}_X[a(x, X)] = \mathbb{E}_X[a(x, X)] - f(x)$

смещение (bias) предсказания алгоритма в точке , усреднённого по всем возможным обучающим выборкам, относительно истинной зависимости
$\text{Var}_X[a(x, X)] = \mathbb{E}_X\left[(a(x, X) - \mathbb{E}_X[a(x, X)])^2\right]$
дисперсия (variance) предсказаний алгоритма в зависимости от обучающей выборки

$\sigma^2 = \mathbb{E}_x \mathbb{E}_\varepsilon \left[ y(x, \varepsilon) - f(x) \right]^2$

неустранимый шум в данных.

🔬 Подробный разбор

Сначала наслаждаемся MLU-explAIn и потом идем читать с выводами формул хендбук

💻 Bias–Variance разложение на настоящем примере. Множество предсказаний моделей в одном классе сложности и усреднение.

Мы обучим деревья решений на выборке (линейная модель) с шумом и посмотрим, как меняются смещение, дисперсия и шум в зависимости от глубины дерева. А также визуализируем, как ведут себя отдельные модели и их усреднение.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_regression
from sklearn.tree import DecisionTreeRegressor
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.utils import resample

# --- Данные
X_all, y_all = make_regression(n_samples=1000, n_features=1, noise=15, random_state=42)
X_train, X_val, y_train, y_val = train_test_split(X_all, y_all, test_size=0.3, random_state=42)
X_clean, y_clean = make_regression(n_samples=300, n_features=1, noise=0, random_state=42)
true_model = LinearRegression().fit(X_clean, y_clean)

X_test = np.linspace(X_all.min(), X_all.max(), 200).reshape(-1, 1)
true_y = true_model.predict(X_test)

# --- Bias², Variance, Noise
depths = range(1, 20)
n_models = 100
biases, variances, noises = [], [], []
models_by_depth = {d: [] for d in [1, 4, 10]}

for d in depths:
    preds = []
    for _ in range(n_models):
        X_boot, y_boot = resample(X_train, y_train)
        model = DecisionTreeRegressor(max_depth=d)
        model.fit(X_boot, y_boot)
        y_pred = model.predict(X_test)
        preds.append(y_pred)
        if d in models_by_depth and len(models_by_depth[d]) < 50:
            models_by_depth[d].append(y_pred)
    preds = np.array(preds)
    mean_preds = preds.mean(axis=0)
    bias2 = ((mean_preds - true_y) ** 2).mean()
    var = preds.var(axis=0).mean()
    noise = np.var(y_val - model.predict(X_val))  # приближённо
    biases.append(bias2)
    variances.append(var)
    noises.append(noise)

# --- График ошибок
plt.figure(figsize=(10, 6))
plt.plot(depths, biases, label='Bias²')
plt.plot(depths, variances, label='Variance')
plt.plot(depths, noises, label='Noise (приближённо)')
plt.plot(depths, np.array(biases) + np.array(variances) + np.array(noises),
         label='Total Error', linestyle='--')
plt.xlabel("Глубина дерева")
plt.ylabel("Ошибка")
plt.title("Bias-Variance Trade-off")
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

Теперь визуализируем сами модели: нарисуем все деревья на разных глубинах, их усреднение и настоящую функцию.

# --- Визуализация моделей
fig, axes = plt.subplots(1, 3, figsize=(18, 5), sharey=True)
for ax, d in zip(axes, [1, 4, 10]):
    all_preds = np.array(models_by_depth[d])
    for y_pred in all_preds:
        ax.plot(X_test.ravel(), y_pred, color='gray', alpha=0.2)
    ax.plot(X_test.ravel(), all_preds.mean(axis=0), color='blue', linewidth=2, label='Усреднённая модель')
    ax.plot(X_test.ravel(), true_y, color='green', linestyle='--', label='f(x) (истинная)')
    ax.scatter(X_train, y_train, s=10, color='black', alpha=0.6, label='Train data')
    ax.set_title(f"Глубина дерева = {d}")
    ax.set_xlabel("x")
    ax.legend()
    ax.grid(True)

axes[0].set_ylabel("y")
plt.suptitle("Смещение и дисперсия на примере деревьев")
plt.tight_layout()
plt.show()

И наконец — как устроены сами данные. Train/test и истинная f(x)

# Визуализация обучающих и тестовых данных на фоне регрессионной прямой
plt.figure(figsize=(8, 5))

# Линия истинной функции
plt.plot(X_test, true_y, color='green', linestyle='--', label='f(x) (истинная)')

# Обучающие и тестовые данные
plt.scatter(X_train, y_train, color='black', s=20, alpha=0.7, label='Train')
plt.scatter(X_val, y_val, color='red', s=20, alpha=0.5, label='Test')

plt.xlabel("x")
plt.ylabel("y")
plt.title("Генерация и распределение данных")
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()

15. Процедура построения дерева решений (Decision tree).

📌 Краткий ответ

Дерево решений строится итеративно, разбивая множество объектов в узле на 2 подмножества по признаку x_j и порогу , чтобы максимально уменьшить информативность (impurity) (чем ниже, тем обьекты ближе можно представить константным значением):

Процедура разбиения узла:

Перебираются все признаки и возможные пороги . Все элементы с признаком меньше порога попадают в левый узел, остальные вправо.
Для каждого разбиения вычисляется:

$\text{Impurity} = \frac{n_\text{left}}{n} \cdot I(D_\text{left}) + \frac{n_\text{right}}{n} \cdot I(D_\text{right})$

где $I(\cdot)$ — функция impurity:

Джини или энтропия (классификация)
- $\text{Gini}(p) = \sum_{k=1}^{K} p_k (1 - p_k) = 1 - \sum_{k=1}^{K} p_k^2$
- $\text{Entropy}(p) = - \sum_{k=1}^{K} p_k \log_2 p_k$
дисперсия (регрессия)
- $\text{MSE}(D) = \frac{1}{n} \sum_{i=1}^{n} (y_i - \bar{y})^2$

Выбирается разбиение с наименьшей информативностью

После разбиения:

В каждом потомке заново пересчитывается "ответ" узла:
- мода (класс) для классификации
- среднее значение для регрессии

Разбиение продолжается рекурсивно, пока не выполнены условия остановки:

достигнута макс. глубина
мало объектов (min_samples_split)
impurity = 0

Важно: дерево строится жадно, локально оптимизируя на каждом шаге, не гарантируя глобального оптимума.

Важность для каждого признака считается так: берут изменение информативности для каждого узла и усредняется на кол-во всех разбиений.

Вопросы на подумать:

Почему важно информативность поправлять на размер узла?
Почему изменение информативности на каждом шаге не отрицательна?
Как эффективно перебирать пороги?

🔬 Подробный разбор

Читаем хендбук или более визуально

💻 Пишем свое дерево решения и сравниваем с sklearn.

tldr:

Видно, что качество по метрики выбиваем такое же
А вот, то что важность у признаков так отличается интересно.


import numpy as np
import pandas as pd
from sklearn.datasets import load_breast_cancer
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
import matplotlib.pyplot as plt

# Загружаем датасет
data = load_breast_cancer()
X, y = data.data, data.target
feature_names = data.feature_names
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

# Свое дерево решений
class Node:
    def __init__(self, gini, samples, value, feature_index=None, threshold=None, left=None, right=None):
        self.gini = gini
        self.samples = samples
        self.value = value
        self.feature_index = feature_index
        self.threshold = threshold
        self.left = left
        self.right = right

class MyDecisionTreeClassifier:
    def __init__(self, max_depth=3, min_samples_split=2):
        self.max_depth = max_depth
        self.min_samples_split = min_samples_split
        self.feature_importances_ = None
        self.tree_ = None

    def fit(self, X, y):
        self.n_classes_ = len(set(y))
        self.n_features_ = X.shape[1]
        self.feature_importances_ = np.zeros(self.n_features_)
        self.tree_ = self._grow_tree(X, y)
    
    def _gini(self, y):
        m = len(y)
        return 1.0 - sum((np.sum(y == c) / m) ** 2 for c in np.unique(y))

    def _best_split(self, X, y):
        m, n = X.shape
        if m <= 1:
            return None, None

        best_gini = 1.0
        best_idx, best_thr = None, None
        parent_gini = self._gini(y)

        for idx in range(n):
            thresholds, classes = zip(*sorted(zip(X[:, idx], y)))
            num_left = [0] * self.n_classes_
            num_right = np.bincount(classes, minlength=self.n_classes_)
            for i in range(1, m):
                c = classes[i - 1]
                num_left[c] += 1
                num_right[c] -= 1
                gini_left = 1.0 - sum((num_left[x] / i) ** 2 for x in range(self.n_classes_))
                gini_right = 1.0 - sum((num_right[x] / (m - i)) ** 2 for x in range(self.n_classes_))
                gini = (i * gini_left + (m - i) * gini_right) / m

                if thresholds[i] == thresholds[i - 1]:
                    continue

                if gini < best_gini:
                    best_gini = gini
                    best_idx = idx
                    best_thr = (thresholds[i] + thresholds[i - 1]) / 2
                    impurity_reduction = parent_gini - gini
                    self.feature_importances_[idx] += impurity_reduction

        return best_idx, best_thr

    def _grow_tree(self, X, y, depth=0):
        num_samples_per_class = [np.sum(y == i) for i in range(self.n_classes_)]
        predicted_class = np.argmax(num_samples_per_class)
        node = Node(
            gini=self._gini(y),
            samples=len(y),
            value=num_samples_per_class
        )

        if depth < self.max_depth and len(y) >= self.min_samples_split and node.gini > 0:
            idx, thr = self._best_split(X, y)
            if idx is not None:
                indices_left = X[:, idx] <= thr
                X_left, y_left = X[indices_left], y[indices_left]
                X_right, y_right = X[~indices_left], y[~indices_left]
                node.feature_index = idx
                node.threshold = thr
                node.left = self._grow_tree(X_left, y_left, depth + 1)
                node.right = self._grow_tree(X_right, y_right, depth + 1)
        return node

    def _predict(self, inputs):
        node = self.tree_
        while node.left:
            if inputs[node.feature_index] <= node.threshold:
                node = node.left
            else:
                node = node.right
        return np.argmax(node.value)

    def predict(self, X):
        return np.array([self._predict(inputs) for inputs in X])

# Обучение и сравнение
my_tree = MyDecisionTreeClassifier(max_depth=3)
my_tree.fit(X_train, y_train)
y_pred_my = my_tree.predict(X_test)

sk_tree = DecisionTreeClassifier(max_depth=3, random_state=42)
sk_tree.fit(X_train, y_train)
y_pred_sk = sk_tree.predict(X_test)

# Сравнение результатов
acc_my = accuracy_score(y_test, y_pred_my)
acc_sk = accuracy_score(y_test, y_pred_sk)
print(f"{acc_my=} {acc_sk=}")
# acc_my=0.9590643274853801 acc_sk=0.9649122807017544


importances_df = pd.DataFrame({
    "Feature": feature_names,
    "MyTree": my_tree.feature_importances_ / np.sum(my_tree.feature_importances_),
    "Sklearn": sk_tree.feature_importances_
}).sort_values(by="MyTree", ascending=False)

importances_df

# Feature	MyTree	Sklearn
# 0	mean radius	0.637033	0.000000
# 7	mean concave points	0.260352	0.809978
# 2	mean perimeter	0.031954	0.000000
# 1	mean texture	0.030274	0.025169
# 6	mean concavity	0.020749	0.000000
# 20	worst radius	0.009949	0.043482
# 21	worst texture	0.002868	0.066145
# 23	worst area	0.001924	0.040310
# 22	worst perimeter	0.001833	0.000000
# 3	mean area	0.001694	0.000000
# 10	radius error	0.001371	0.000000

16. Критерии информации. Критерии энтропии, неопределенности Джини.

📌 Краткий ответ

Смотри предыдущий пункт. Самое главное понимать, что максимум функции (информативности) достигается, когда всех обьектов поровну, а минимум все бъекты одного класса.

График функций информативности для двух классов

💻 Визуализируем критерии информативности

import numpy as np
import matplotlib.pyplot as plt

# Вероятности для одного из классов (например, класс 1)
p = np.linspace(0, 1, 500)

# Энтропия (Shannon entropy)
entropy = -p * np.log2(p + 1e-9) - (1 - p) * np.log2(1 - p + 1e-9)

# Джини
gini = 2 * p * (1 - p)

# Визуализация
plt.figure(figsize=(8, 5))
plt.plot(p, entropy, label='Entropy', linewidth=2)
plt.plot(p, gini, label='Gini Impurity', linewidth=2)
plt.xlabel("p (доля одного класса)")
plt.ylabel("Impurity")
plt.title("Сравнение критериев информации")
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

График функций информативности для двух классов

17. Ансамблевые методы. Бутстрап (bootstrap). Бэггинг (bagging). Стекинг (stacking)

📌 Краткий ответ

Ансамбли — это способ объединить множество простых моделей, чтобы получить одну, более устойчивую.

Бутстрап: процесс генерации подвыборок с помощью семплирования с возвращением.

Бэггинг (bagging, bootstrap aggregation) - обучаем несколько моделей на бутстрап-выборках и агрегируем их ответы (усреднение или голосование).

Теория вокруг Bias-variance trade-off говорит, что смещение (bias) не изменится, a дисперсия (variance) уменьшится в k раз (Если предположить независимость базовых алгоритмов). Вывод утверждения для задачи регрессии. $\Rightarrow$ берем сложные, глубокие модели, чтобы уменьшить смещение (а дисперсию уменьшим с помощью беггинга!)

Стекинг (stacking): 1. Учим несколько (разной природы) моделей на разных фолдах, и потом на отдельном фолде учим мета модель .

Например:

Случайный лес (Random Forest) = бэггинг + метод случайных подпространств(=в каждом узле дерева выбирается случайное подмножество признаков):

Из какого кол-во признаков выбирать?

Много признаков $\Rightarrow$ большая скоррелированность моделей (=маленький эффект от ансамблирования).
Мало признаков $\Rightarrow$ модели слабые (=смещение увеличивается).

Практическая рекомендация — брать корень из числа всех признаков для классификации и треть признаков для регрессии.

🔬 Подробный разбор

Хендбук + визуализация

💻 Сравнения ансамблёвых моделей


# Импорт всех нужных библиотек
from sklearn.ensemble import (
    BaggingClassifier,
    StackingClassifier,
    RandomForestClassifier,
    GradientBoostingClassifier
)
from sklearn.tree import DecisionTreeClassifier
from sklearn.linear_model import LogisticRegression
from sklearn.svm import SVC
from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
import matplotlib.pyplot as plt

# Загружаем датасет
X, y = load_breast_cancer(return_X_y=True)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

# 1. Обычное дерево
tree = DecisionTreeClassifier(random_state=42)
tree.fit(X_train, y_train)
y_pred_tree = tree.predict(X_test)
acc_tree = accuracy_score(y_test, y_pred_tree)

# 2. Бэггинг
bag = BaggingClassifier(DecisionTreeClassifier(), n_estimators=100, random_state=42)
bag.fit(X_train, y_train)
y_pred_bag = bag.predict(X_test)
acc_bag = accuracy_score(y_test, y_pred_bag)

# 3. Стекинг: дерево + SVM → логрегрессия
stack = StackingClassifier(
    estimators=[
        ("dt", DecisionTreeClassifier()),
        ("svm", SVC(probability=True))
    ],
    final_estimator=LogisticRegression(),
    cv=5
)
stack.fit(X_train, y_train)
y_pred_stack = stack.predict(X_test)
acc_stack = accuracy_score(y_test, y_pred_stack)

# 4. Случайный лес
rf = RandomForestClassifier(n_estimators=100, random_state=42)
rf.fit(X_train, y_train)
y_pred_rf = rf.predict(X_test)
acc_rf = accuracy_score(y_test, y_pred_rf)

# 5. Градиентный бустинг
boost = GradientBoostingClassifier(n_estimators=100, learning_rate=0.1, max_depth=3, random_state=42)
boost.fit(X_train, y_train)
y_pred_boost = boost.predict(X_test)
acc_boost = accuracy_score(y_test, y_pred_boost)

# Визуализация результатов
models = ['Decision Tree', 'Bagging', 'Stacking', 'Random Forest', 'Boosting']
accuracies = [acc_tree, acc_bag, acc_stack, acc_rf, acc_boost]

plt.figure(figsize=(10, 5))
plt.bar(models, accuracies, color=['skyblue', 'lightgreen', 'salmon', 'gold', 'orchid'])
plt.ylim(0.9, 1.0)
plt.ylabel("Accuracy")
plt.title("Сравнение ансамблевых моделей на Breast Cancer Dataset")
plt.grid(axis='y')
plt.tight_layout()
plt.show()

# Вывод точности всех моделей
acc_tree, acc_bag, acc_stack, acc_rf, acc_boost
# (0.9415204678362573,
#  0.9590643274853801,
#  0.9649122807017544,
#  0.9707602339181286,
#  0.9590643274853801)

18. Случайный лес (Random Forest), метод случайных подпространств.

📌 Краткий ответ

Смотри прошлый билет!

💻 Поиск оптимального кол-ва случайных признаков. Несогласованность и точность моделей.

Видим, как с увеличением случайных признаков увеличивается согласованность ответов $\Rightarrow$ модели становятся скоррелированны $\Rightarrow$ качество бесконечно не растет
.


# Будем оценивать дисперсию (variance) предсказаний разных деревьев
# для каждого значения max_features

tree_variances = []
mean_accuracies = []
max_features_range = range(1, n_features + 1)

for mf in max_features_range:
    rf = RandomForestClassifier(
        n_estimators=100, max_features=mf, random_state=42, oob_score=False
    )
    rf.fit(X_train, y_train)
    
    # Предсказания всех деревьев
    all_preds = np.array([tree.predict(X_test) for tree in rf.estimators_])  # shape (n_estimators, n_samples)
    
    # Среднее предсказание (majority vote)
    majority_vote = np.round(np.mean(all_preds, axis=0)).astype(int)
    acc = accuracy_score(y_test, majority_vote)
    mean_accuracies.append(acc)
    
    # Оценка "дисперсии" (простейшая: средняя доля несогласия между деревьями)
    disagreement = np.mean(np.var(all_preds, axis=0))
    tree_variances.append(disagreement)

# Визуализация
fig, ax1 = plt.subplots(figsize=(10, 5))

color = 'tab:blue'
ax1.set_xlabel("max_features")
ax1.set_ylabel("Disagreement (Variance across trees)", color=color)
ax1.plot(max_features_range, tree_variances, color=color, label="Variance across trees")
ax1.tick_params(axis='y', labelcolor=color)
ax1.grid(True)

ax2 = ax1.twinx()
color = 'tab:green'
ax2.set_ylabel("Accuracy", color=color)
ax2.plot(max_features_range, mean_accuracies, color=color, linestyle='--', label="Accuracy")
ax2.tick_params(axis='y', labelcolor=color)

plt.title("Variance across trees vs Accuracy (Random Forest)")
fig.tight_layout()
plt.show()

19. Бустинг и градиентный бустинг (Gradient Boosting). Основная идея, производная градиента.

📌 Краткий ответ

Бустинг — это ансамблевый метод, в котором модели обучаются последовательно, каждая новая модель пытается исправить ошибки предыдущих.

В отличие от бэггинга (параллельные модели), здесь идет цепочка из "корректоров".
Итоговое предсказание — взвешенная сумма всех слабых моделей.

Градиентный бустинг (Gradient Boosting) — это частный случай, где каждая новая модель аппроксимирует антиградиент функции потерь (напр. MSE, логлосс) по предсказаниям текущего ансамбля.

🔬 Подробный разбор

📘 Общая идея бустинга

Очень круто, подробно и просто описано тут.

Имеем задачу регрессии или классификации с функцией потерь L(y, F(x)) .
Хотим построить итоговую модель в виде:

$F(x) = \sum_{m=1}^{M} \gamma_m h_m(x)$

Каждый новый слабый алгоритм h_m(x) обучается на остатках или антиградиенте предыдущей ошибки.

Градиентный бустинг (Gradient Boosting)

На шаге строим новую модель h_m , которая аппроксимирует антиградиент функции потерь по текущим предсказаниям:

$r_i^{(m)} = - \left. \frac{\partial L(y_i, F(x_i))}{\partial F(x_i)} \right|_{F = F_{m-1}}$

После этого:

обучаем на $(x_i, r_i^{(m)})$
выбираем шаг $\gamma_m$
обновляем:
$F_m(x) = F_{m-1}(x) + \gamma_m h_m(x)$

Примеры градиентов:

MSE (регрессия):
$\frac{\partial}{\partial F(x)} \frac{1}{2}(y - F(x))^2 = F(x) - y\Rightarrow r_i = y_i - F(x_i)$
То есть просто остатки! Совпадает с определением бустинга.
Log-loss (бинарная классификация):
$L(y, F) = \log(1 + e^{-yF}) \Rightarrow r_i = \frac{-y_i}{1 + e^{y_i F(x_i)}}$

Почему работает?

Рассматриваем задачу не как минимизация расстояния между вектором предсказания и истинных значений, а с точки зрения функции потерь!
Итеративно минимизируем функцию потерь — как градиентный спуск в функциональном пространстве (в мерном пространстве, - размер датасета). Каждый шаг - это добавление антиградиента к аргументу функции $\Rightarrow$ уменьшение лосса.
Для MSE это одно и тоже! (остаток и антиградиент равны)

Решение задачи как минимизация расстояния предсказания и истины

Решение задачи как минимизация функции потерь

Обращу внимание, тот и тот оба решает задачу, только второй это делает по наискорейшему направлению.

А как выбрать базовые модели? Берутся "простые" модели (с низкой дисперсией), и итеративно уменьшается смещение

Основные реализации, работающие в проде. XGBoost, LightGBM и CatBoost.
Очень важно знать важные фишки и отличия.

💻 Реализовываем свой градиентный бустинг. Сравниваемся с GradientBoostingRegressor и RandomForestRegressor.

Получился код, с таким же качеством как из sklearn.
Дерево решение проиграло бустингу.

# Полный код: сравнение градиентного бустинга и случайного леса

import numpy as np
import matplotlib.pyplot as plt
from sklearn.tree import DecisionTreeRegressor
from sklearn.metrics import mean_squared_error
from sklearn.model_selection import train_test_split
from sklearn.ensemble import GradientBoostingRegressor, RandomForestRegressor

# 1. Синтетические данные
np.random.seed(42)
X = np.linspace(0, 10, 500).reshape(-1, 1)
y_true = np.sin(X).ravel()
y = y_true + np.random.normal(0, 0.3, size=X.shape[0])
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

# 2. Собственный градиентный бустинг
class MyGradientBoostingRegressor:
    def __init__(self, n_estimators=100, learning_rate=0.1, max_depth=3):
        self.n_estimators = n_estimators
        self.learning_rate = learning_rate
        self.max_depth = max_depth
        self.models = []
        self.gammas = []

    def fit(self, X, y):
        self.models = []
        self.gammas = []
        self.init_val = np.mean(y)
        F = np.full_like(y, fill_value=self.init_val, dtype=np.float64)

        for m in range(self.n_estimators):
            residuals = y - F
            tree = DecisionTreeRegressor(max_depth=self.max_depth)
            tree.fit(X, residuals)
            prediction = tree.predict(X)
            gamma = 1.0
            F += self.learning_rate * gamma * prediction
            self.models.append(tree)
            self.gammas.append(gamma)

    def predict(self, X):
        F = np.full(X.shape[0], self.init_val)
        for gamma, tree in zip(self.gammas, self.models):
            F += self.learning_rate * gamma * tree.predict(X)
        return F

# 3. Обучение всех моделей
# Собственный бустинг
my_gb = MyGradientBoostingRegressor(n_estimators=100, learning_rate=0.1, max_depth=3)
my_gb.fit(X_train, y_train)
y_pred_my = my_gb.predict(X_test)
mse_my = mean_squared_error(y_test, y_pred_my)

# sklearn GB (обычный)
sklearn_gb = GradientBoostingRegressor(n_estimators=100, learning_rate=0.1, max_depth=3, random_state=42)
sklearn_gb.fit(X_train, y_train)
y_pred_sklearn = sklearn_gb.predict(X_test)
mse_sklearn = mean_squared_error(y_test, y_pred_sklearn)

# sklearn GB (низкий learning_rate)
sklearn_gb_slow = GradientBoostingRegressor(n_estimators=300, learning_rate=0.03, max_depth=3, random_state=42)
sklearn_gb_slow.fit(X_train, y_train)
y_pred_slow = sklearn_gb_slow.predict(X_test)
mse_slow = mean_squared_error(y_test, y_pred_slow)

# Случайный лес
rf = RandomForestRegressor(n_estimators=100, max_depth=6, random_state=42)
rf.fit(X_train, y_train)
y_pred_rf = rf.predict(X_test)
mse_rf = mean_squared_error(y_test, y_pred_rf)

# 4. Сортировка для гладких графиков
sorted_idx = np.argsort(X_test.ravel())
X_plot = X_test[sorted_idx]
y_true_plot = np.sin(X_plot).ravel()
y_test_plot = y_test[sorted_idx]
y_pred_my_plot = y_pred_my[sorted_idx]
y_pred_sklearn_plot = y_pred_sklearn[sorted_idx]
y_pred_slow_plot = y_pred_slow[sorted_idx]
y_pred_rf_plot = y_pred_rf[sorted_idx]

# 5. Визуализация
plt.figure(figsize=(12, 6))
plt.plot(X_plot, y_true_plot, label="True function sin(x)", color='green', linestyle='--')
plt.plot(X_plot, y_pred_my_plot, label=f"My GB (MSE={mse_my:.4f})", color='red')
plt.plot(X_plot, y_pred_sklearn_plot, label=f"sklearn GB (0.1) (MSE={mse_sklearn:.4f})", color='blue')
plt.plot(X_plot, y_pred_slow_plot, label=f"sklearn GB (0.03) (MSE={mse_slow:.4f})", color='orange')
plt.plot(X_plot, y_pred_rf_plot, label=f"Random Forest (MSE={mse_rf:.4f})", color='purple')
plt.scatter(X_plot, y_test_plot, label="Test data", s=10, alpha=0.3)
plt.legend()
plt.title("Сравнение бустинга (ручной и sklearn) и случайного леса")
plt.grid(True)
plt.tight_layout()
plt.show()

Что дальше?

Вдумчиво разбираемся в вопросах, но коротко и понятно рассказываем суть.

Следующий этап - уметь, понимая базу, отвечать на каверзные вопросы. Поэтому сохраняем их для будущей тренировки!

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 — начнем с ввода в глубокое обучение, а закончим разбором важнейших классических архитектур. Пока подписывайтесь и делитесь своими находками!

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23 июн. 2025 г.

12.09.25 15:06 michaeldavenport218

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12.09.25 15:06 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
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14.09.25 12:44 robertalfred175

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14.09.25 17:48 robertalfred175

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14.09.25 20:49 Clinton

I know firsthand how devastating it feels to lose money to a scam. When it happened to me, I was left frustrated, hopeless, and unsure where to turn. Complaining to apps about being scammed on their platforms didn’t change anything it felt like no one cared. But through a friend’s advice, I connected with a recovery professional who gave me real hope. With their help, I was able to get my funds back, something I thought was impossible. I’m sharing this because I don’t want anyone else to feel as lost as I once did. Whether you’ve been scammed through crypto platforms, dating scams, real-estate or mortgage fraud, or even fake ICOs, please know there’s still a way forward. If you’ve lost money, reach out to ([email protected]) or (WhatsApp) at (+)44 7366445035 for consultation and recovery services.
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15.09.25 12:49 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
15.09.25 12:49 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
15.09.25 12:49 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
16.09.25 12:25 aliceforemanlaw

Sylvester Bryant helped me recover 120,000 in Ethereum. You can reach him at Yt7cracker@gmail. com. It was a great experience overall. I really suggest Mr. Sylvester. He helps people who lost money. He is great at getting money back from scams. Scammers cause a lot of stress and hurt. Mr. Bryant offers an important service. He can help you get back stolen funds. He was very professional and earned my trust. Contact him if you lost money to scams. He is also on WhatsApp at +1 512 577 7957. This makes it easy to talk about your situation. Getting this amount back was tough. Mr. Bryant knew a lot about the technical parts. His drive to fix these issues is clear. Get his help if you lost crypto or other digital items. Many people worry about this. Getting expert help can really make a difference.
16.09.25 12:26 aliceforemanlaw

Sylvester Bryant helped me recover 120,000 in Ethereum. You can reach him at Yt7cracker@gmail. com. It was a great experience overall. I really suggest Mr. Sylvester. He helps people who lost money. He is great at getting money back from scams. Scammers cause a lot of stress and hurt. Mr. Bryant offers an important service. He can help you get back stolen funds. He was very professional and earned my trust. Contact him if you lost money to scams. He is also on WhatsApp at +1 512 577 7957. This makes it easy to talk about your situation. Getting this amount back was tough. Mr. Bryant knew a lot about the technical parts. His drive to fix these issues is clear. Get his help if you lost crypto or other digital items. Many people worry about this. Getting expert help can really make a difference.
16.09.25 13:25 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
16.09.25 13:25 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.09.25 02:56 peju1213

It can be very concerning to lose access to your USDT (Tether) wallet. It could potentially result in permanent loss of significant funds. You may have misplaced your private keys. Perhaps you unintentionally erased something, or your security was breached. It seems hopeless when you are unable to access your USDT. However, it doesn't have to stop there. There are methods for recovering your lost USDT. During difficult circumstances, professional assistance and wise recuperation techniques can give you hope. get in touch with Marie ([email protected] and +1 7127594675) on WhatsApp.
17.09.25 11:16 [email protected]

Sylvester Bryant helped me recover $510,000 in Ethereum, and I highly recommend his services. He specializes in helping people recover funds lost to scams. Scammers can cause significant stress, but Mr. Bryant's professionalism and expertise in the technical aspects of recovery earned my trust. If you've lost money through scams, you can reach him at [ yt7cracker@gmail. com ] or on WhatsApp at +1 512 577 7957. His dedication to helping people get their stolen funds back is clear, and his support made a huge difference in my case.
17.09.25 11:16 [email protected]

Sylvester Bryant helped me recover $510,000 in Ethereum, and I highly recommend his services. He specializes in helping people recover funds lost to scams. Scammers can cause significant stress, but Mr. Bryant's professionalism and expertise in the technical aspects of recovery earned my trust. If you've lost money through scams, you can reach him at [ yt7cracker@gmail. com ] or on WhatsApp at +1 512 577 7957. His dedication to helping people get their stolen funds back is clear, and his support made a huge difference in my case.
17.09.25 23:50 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.09.25 23:50 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.09.25 23:50 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
18.09.25 11:55 Mundo

Sylvester Bryant recovered £400,000 in Ethereum for me. I strongly advise using his services. He focuses on retrieving money lost to fraudulent schemes. Scams cause immense worry. Mr. Bryant's expert knowledge and calm approach in getting funds back reassured me. If you have lost money to scams, contact him via email at [email protected]. You can also reach him on WhatsApp at +1 512 577 7957. He is committed to helping people recover their stolen assets. His support was invaluable in my situation.
18.09.25 11:55 Mundo

Sylvester Bryant recovered £400,000 in Ethereum for me. I strongly advise using his services. He focuses on retrieving money lost to fraudulent schemes. Scams cause immense worry. Mr. Bryant's expert knowledge and calm approach in getting funds back reassured me. If you have lost money to scams, contact him via email at [email protected]. You can also reach him on WhatsApp at +1 512 577 7957. He is committed to helping people recover their stolen assets. His support was invaluable in my situation.
18.09.25 12:22 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
18.09.25 12:22 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
18.09.25 13:04 Mundo

Sylvester Bryant recovered £400,000 in Ethereum for me. I strongly advise using his services. He focuses on retrieving money lost to fraudulent schemes. Scams cause immense worry. Mr. Bryant's expert knowledge and calm approach in getting funds back reassured me. If you have lost money to scams, contact him via email at [email protected]. You can also reach him on WhatsApp at +1 512 577 7957. He is committed to helping people recover their stolen assets. His support was invaluable in my situation.
18.09.25 16:46 carolinehudso83

I noticed a lot of online recommendations, and it’s clear that some of them are bad eggs that will just make уour mуsterу worse. I can onlу suggest one, and if уou need assistance getting back the moneу уou lost to scammers, уou can contact them bу email at: [email protected] Whats app or text +1 518 468 2985 Website https://bestrecoveryagent.com/
19.09.25 00:54 frank2025

Anthony davies played a crucial role in successfully recovering my stolen USDT, which was valued at more than $300,000. His expertise and dedication made the recovery process smooth and efficient. Throughout the entire time, he demonstrated himself to be a reliable recovery agent. His professionalism and commitment to his clients are evident in the results he achieves. If you find yourself in a similar situation or need assistance, he is available for contact. You can reach anthony through email at (anthonydaviestech AT gmail dot com). Alternatively, he is also accessible via telegram at anthonydavies01. Reaching out to him could be the first step toward recovering your lost assets
19.09.25 10:02 faithlawrence

Sylvester Bryant recovered £400,000 in Ethereum for me. I strongly advise using his services. He focuses on retrieving money lost to fraudulent schemes. Scams cause immense worry. Mr. Bryant's expert knowledge and calm approach in getting funds back reassured me. If you have lost money to scams, contact him via email at [email protected]. You can also reach him on WhatsApp at +1 512 577 7957. He is committed to helping people recover their stolen assets. His support was invaluable in my situation.
19.09.25 10:02 faithlawrence

Sylvester Bryant recovered £400,000 in Ethereum for me. I strongly advise using his services. He focuses on retrieving money lost to fraudulent schemes. Scams cause immense worry. Mr. Bryant's expert knowledge and calm approach in getting funds back reassured me. If you have lost money to scams, contact him via email at [email protected]. You can also reach him on WhatsApp at +1 512 577 7957. He is committed to helping people recover their stolen assets. His support was invaluable in my situation.
19.09.25 15:27 tonykith01477

There are not many reviews about free crypto recovery fixed but the ones that exist are mostly positive. I have no idea how that is possible, but it is clear that they are fabricated. However, there are also negative reviews – and I highly recommend paying attention to them. These are real people describing their unfortunate experiences with this scam. It’s the same story as always – fraudsters create a fake website to con people out of money. Nothing new but look no more and contact FASTRECOVERYAGENT These types of scams are everywhere. If you have already lost money to scammers i mean any type be it sending to scammers account , or if you have a case about stolen bitcoin , usdt, or any type of cryptocurrency whatsoever just reach out to www.fastrecoveryagent.com, i really owe this group of recovery expert because they saved me after bad investment with a fake broker, i literally owe them my life as they saved me from some bunch of scammers, but see how life is , i got every cent of my investment back with the profit , reach out to to them today and tell them from Mary because i promise them i will tell the whole world when the recovery is complete, and here i go after i got my recovered assets thats why im doing what i promised. do not fall for another scam. contact the,m today!!!!
19.09.25 17:12 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
19.09.25 17:12 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
20.09.25 15:05 faithlawrence

I can’t recommend Sylvester Bryant enough. He successfully recovered €210,000 in Ethereum for me after I had lost hope. His expertise in tracing and reclaiming funds from scams is truly remarkable. What stood out most was his calm, professional approach and deep technical knowledge, which gave me complete confidence throughout the process. If you’ve lost money to a scam, I strongly encourage you to reach out to him. You can contact him via email at [[email protected] ] or on WhatsApp at +1 512 577 7957. He is genuinely dedicated to helping people recover what they’ve lost, and his support has been invaluable to me.
20.09.25 15:53 blessing1198

It is distressing to lose USDT due to a bitcoin wallet hack. Although it is challenging, stolen USDT can be recovered. Taking prompt, wise action increases your chances. Marie can help you with reporting the theft, what to do right away, and USDT recovery. Contact her on WhatsApp at +1 7127594675, or email [email protected].
21.09.25 12:05 star1121

Consider this: In cryptocurrency, you see what appears to be a fantastic opportunity. After investing your hard-earned money, you see it disappear into the wallet of a con artist. Your bank account seems empty as rage and regret merge in this stomach punch. These days, cryptocurrency frauds are very common, however recovering your cryptocurrency from scammers is still possible. You can track down and possibly recover what you lost with shrewd actions. Marie can help; contact her at [email protected] and on WhatsApp at +1 7127594675.
23.09.25 03:23 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
23.09.25 03:23 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
23.09.25 03:23 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
23.09.25 03:54 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
23.09.25 14:45 Raymondkrisitina

Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.
23.09.25 19:27 beverlyalex010

In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider [email protected] WhatsApp at +44 736-644-5035 through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and I’m endlessly grateful.
23.09.25 22:38 Raymondkrisitina

Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.
24.09.25 12:22 beverlyalex010

In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider [email protected] WhatsApp at +44 736-644-5035 through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and I’m endlessly grateful.
24.09.25 15:50 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
24.09.25 15:50 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
24.09.25 15:50 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
24.09.25 19:08 Raymondkrisitina

Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.
24.09.25 19:50 Raymondkrisitina

Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.
24.09.25 19:55 Athea5130

ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)
24.09.25 19:56 Athea5130

ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)
24.09.25 19:56 Athea5130

ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)
24.09.25 19:56 Athea5130

ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)
24.09.25 20:52 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
24.09.25 20:52 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
26.09.25 12:29 beverlyalex010

In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider (recoveryfundprovider @ gmail. com WhatsApp +44 736-644-5035) through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and i am endlessly grateful.
26.09.25 15:42 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
26.09.25 15:42 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
26.09.25 16:40 Slimbella

I fully recommend Sylvester Bryant. He recovered €230,000 in Ethereum for me after I believed it was lost for good. His talent for tracing and reclaiming funds stolen by scammers impresses me deeply. I valued his calm, skilled approach and solid grasp of technology. This gained my confidence at every turn. If scammers have stolen your cash, contact him now. Reach out by email at yt7cracker@gmail. com or via WhatsApp at +1 512 577 7957. He dedicates himself to helping people recover their belongings. His support changed everything for me.
26.09.25 16:40 Slimbella

I fully recommend Sylvester Bryant. He recovered €230,000 in Ethereum for me after I believed it was lost for good. His talent for tracing and reclaiming funds stolen by scammers impresses me deeply. I valued his calm, skilled approach and solid grasp of technology. This gained my confidence at every turn. If scammers have stolen your cash, contact him now. Reach out by email at yt7cracker@gmail. com or via WhatsApp at +1 512 577 7957. He dedicates himself to helping people recover their belongings. His support changed everything for me.
26.09.25 19:08 beverlyalex010

In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider ( [email protected]. WhatsApp +44 736-644-5035) through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and i am endlessly grateful.
26.09.25 19:53 carolinehudso83

You are one step away from recovering your lost crypto funds. CAPITAL REDEMPTION WIZARD is the solution. Without them, I would have lost everything. I was scammed through a compromised email, lured by a fake Elon Musk Bitcoin investment. After applying and completing KYC, I was credited with 2.5 Bitcoin. When I tried to withdraw, I was hit with fees, and my wallet was emptied of $103,000.00. Their support team was hostile. I researched and found CAPITAL REDEMPTION WIZARD. They recovered my hacked Bitcoin. I learned the Bitcoin offer was a scam. CAPITAL REDEMPTION WIZARD guided me through this. Email: ( [email protected] ) Whats app or text +1 518 468 2985 Website https://bestrecoveryagent.com/
26.09.25 22:25 Slimbella

I fully recommend Sylvester Bryant. He recovered €230,000 in Ethereum for me after I believed it was lost for good. His talent for tracing and reclaiming funds stolen by scammers impresses me deeply. I valued his calm, skilled approach and solid grasp of technology. This gained my confidence at every turn. If scammers have stolen your cash, contact him now. Reach out by email at yt7cracker@gmail. com or via WhatsApp at +1 512 577 7957. He dedicates himself to helping people recover their belongings. His support changed everything for me.
26.09.25 22:59 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
26.09.25 22:59 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
27.09.25 03:07 Angela_Moore

I thought my money was lost forever. Then Mr. Sylvester stepped in. He tracked down and recovered $107,000 in stablecoins , plus all my earnings. His talent for finding scam-stolen funds left me stunned. I loved how he handled everything with real expertise and solid tech skills. It got my scammed cash back safe. I trusted him completely. If you've lost funds to a scam, reach out to him now. Email [email protected] or text on WhatsApp at +1 512 577 7957. His support saved me.
28.09.25 00:42 Anitastar

Wizard Hilton Cyber Tech's strategic approach to Bitcoin recovery represents a mutually beneficial collaboration that offers valuable advantages for all involved. At the core of this innovative partnership is a shared commitment to leveraging cutting-edge technology and expertise to tackle the increasingly complex challenges of cryptocurrency theft and loss. By combining Wizard Hilton's world-class cybersecurity capabilities with the deep industry insights and recovery methodologies of Cyber Tech, this alliance is poised to revolutionize the way individuals and organizations safeguard their digital assets. Through a meticulous, multi-layered process, the team meticulously analyzes each case, employing advanced forensic techniques to trace the flow of stolen funds and identify potential recovery avenues. This rigorous approach not only maximizes the chances of successful Bitcoin retrieval, but also provides invaluable intelligence to enhance future security measures and prevention strategies. Importantly, the collaboration is built on a foundation of trust, transparency, and a genuine concern for the well-being of clients, ensuring that the recovery process is handled with the utmost care and discretion. As the cryptocurrency landscape continues to evolve, this strategic alliance between Wizard Hilton Cyber Tech stands as a shining example of how industry leaders can come together to safeguard digital assets, protect victims of cybercrime, and pave the way for a more secure and resilient cryptocurrency ecosystem. Email : wizardhiltoncybertech ( @ ) gmail (. ) com OR support ( @ ) wizardhiltoncybertech (.) com WhatsApp number +18737715701 Thanks.
28.09.25 01:48 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
28.09.25 01:48 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
28.09.25 01:49 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.09.25 13:47 thomassankara

USDT recovery expert / company I thought my money was lost forever. Then Mr. Sylvester stepped in. He tracked down and recovered $107,000 in stablecoins , plus all my earnings. His talent for finding scam-stolen funds left me stunned. I loved how he handled everything with real expertise and solid tech skills. It got my scammed cash back safe. I trusted him completely. If you've lost funds to a scam, reach out to him now. Email [email protected] or text on WhatsApp at +1 512 577 7957. His support saved me.
29.09.25 16:32 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
29.09.25 16:32 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
29.09.25 19:46 beverlyalex010

In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider ( recoveryfundprovider@gmail. com WhatsApp +44 736-644-5035) through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and i am endlessly grateful.
29.09.25 21:06 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
29.09.25 21:07 beverlyalex010

I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.
30.09.25 11:02 patricialovick86

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30.09.25 11:02 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
01.10.25 16:51 beverlyalex010

In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider ( [email protected] WhatsApp +44 736-644-5035) through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and I’m endlessly grateful.
01.10.25 17:24 johnn

Anthony davies, renowned for his expertise in recovering stolen cryptocurrency, especially specializing in USDT, provided invaluable assistance in a scenario where a significant sum of $571,000 was taken from me. I had the privilege of witnessing his exceptional skills firsthand and I am truly thankful for his prompt efforts, which led to the successful recovery of the entire amount in just a span of 72 hours. Mr Anthony davies swift reactions and efficient tactics not only resolved my financial troubles but also alleviated much of the stress on my mental well-being. You can reach out to him immediately and get connected with email at anthonydaviestech@gmail com also can be contacted on WhatsApp at +951 490-8435, he is an expert in the field most especially in recovering lost digital assets.
01.10.25 17:25 johnn

Anthony davies, renowned for his expertise in recovering stolen cryptocurrency, especially specializing in USDT, provided invaluable assistance in a scenario where a significant sum of $571,000 was taken from me. I had the privilege of witnessing his exceptional skills firsthand and I am truly thankful for his prompt efforts, which led to the successful recovery of the entire amount in just a span of 72 hours. Mr Anthony davies swift reactions and efficient tactics not only resolved my financial troubles but also alleviated much of the stress on my mental well-being. You can reach out to him immediately and get connected with email at anthonydaviestech@gmail com also can be contacted on WhatsApp at +951 490-8435, he is an expert in the field most especially in recovering lost digital assets.

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Н Новости

Главное по ML/DL, часть 2: Вопрос → Краткий ответ → Разбор → Пример кода. SVD/PCA. Bias-variance. Деревья. Бустинг

11. Анализ главных компонент. Связь с SVD. Теорема Эккарта-Янга. Как применять PCA на практике.

12. Этапы обучения, валидации и тестирования модели. Проблема переобучения, способы её обнаружения.

13. Стратегии валидации. Кросс-валидация. Утечки данных.

14. Компромисс смещения-дисперсии (Bias-variance trade-off). Double Descent.

15. Процедура построения дерева решений (Decision tree).

16. Критерии информации. Критерии энтропии, неопределенности Джини.

17. Ансамблевые методы. Бутстрап (bootstrap). Бэггинг (bagging). Стекинг (stacking)

18. Случайный лес (Random Forest), метод случайных подпространств.

19. Бустинг и градиентный бустинг (Gradient Boosting). Основная идея, производная градиента.

📘 Общая идея бустинга

Градиентный бустинг (Gradient Boosting)

Примеры градиентов:

Почему работает?

Что дальше?

Материалы

Похожие новости

Что будет, если заставить ИИ-агента работать с тысячами API

Глубокие фейки с согласия: в новом приложении Sora можно использовать образы друзей

Stripe представила платформу для запуска стейблкоинов

AI-компаньон для профориентации на хакатоне

Tether докупила биткоинов на $1 млрд

SEC остановила торги акциями биткоин-фирмы QMMM

Н Новости

Главное по ML/DL, часть 2: Вопрос → Краткий ответ → Разбор → Пример кода. SVD/PCA. Bias-variance. Деревья. Бустинг

11. Анализ главных компонент. Связь с SVD. Теорема Эккарта-Янга. Как применять PCA на практике.

12. Этапы обучения, валидации и тестирования модели. Проблема переобучения, способы её обнаружения.

13. Стратегии валидации. Кросс-валидация. Утечки данных.

14. Компромисс смещения-дисперсии (Bias-variance trade-off). Double Descent.

15. Процедура построения дерева решений (Decision tree).

16. Критерии информации. Критерии энтропии, неопределенности Джини.

17. Ансамблевые методы. Бутстрап (bootstrap). Бэггинг (bagging). Стекинг (stacking)

18. Случайный лес (Random Forest), метод случайных подпространств.

19. Бустинг и градиентный бустинг (Gradient Boosting). Основная идея, производная градиента.

📘 Общая идея бустинга

Градиентный бустинг (Gradient Boosting)

Примеры градиентов:

Почему работает?

Что дальше?

Материалы

Похожие новости

Что будет, если заставить ИИ-агента работать с тысячами API

Глубокие фейки с согласия: в новом приложении Sora можно использовать образы друзей

Stripe представила платформу для запуска стейблкоинов

AI-компаньон для профориентации на хакатоне

Tether докупила биткоинов на $1 млрд

SEC остановила торги акциями биткоин-фирмы QMMM

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