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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.

09.10.25 08:23 pHqghUme

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14.10.25 08:46 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
15.10.25 18:07 crypto

Cryptocurrency's digital realm presents many opportunities, but it also conceals complex frauds. It is quite painful to lose your cryptocurrency to scam. You can feel harassed and lost as a result. If you have been the victim of a cryptocurrency scam, this guide explains what to do ASAP. Following these procedures will help you avoid further issues or get your money back. Communication with Marie ([email protected] and WhatsApp: +1 7127594675) can make all the difference.
15.10.25 21:52 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.10.25 21:52 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.10.25 20:17 tyleradams

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17.10.25 20:20 lindseyvonn

Have you gotten yourself involved in a cryptocurrency scam or any scam at all? If yes, know that you are not alone, there are a lot of people in this same situation. I'm a Health Worker and was a victim of a cryptocurrency scam that cost me a lot of money. This happened a few weeks ago, there’s only one solution which is to talk to the right people, if you don’t do this you will end up being really depressed. I was really devastated until went on LinkedIn one evening after my work hours and i saw lots of reviews popped up on my feed about [email protected], I sent an email to the team who came highly recommended - [email protected] I started seeing some hope for myself from the moment I sent them an email. The good part is they made the entire process stress free for me, i literally sat and waited for them to finish and I received what I lost in my wallet
17.10.25 20:22 richardcharles

I would recommend NVIDIA TECH HACKERS to anyone that needs this service. I decided to get into crypto investment and I ended up getting my crypto lost to an investor late last year. The guy who was supposed to be managing my account turned out to be a scammer all along. I invested 56,000 USD and at first, my reading and profit margins were looking good. I started getting worried when I couldn’t make withdrawals and realized that I’ve been scammed. I came across some of the testimonials that people said about NVIDIA TECH HACKERS and how helpful he has been in recovering their funds. I immediately contacted him in his mail at [email protected] so I can get his assistance. One week into the recovery process the funds were traced and recovered back from the scammer. I can't appreciate him enough for his professionalism.
17.10.25 20:23 stevekalfman

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17.10.25 21:42 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
17.10.25 21:42 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
17.10.25 21:42 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
21.10.25 08:39 debby131

Given how swiftly the cryptocurrency market moves, losing USDT may be a terrifying and upsetting experience. Whether you experienced a technical problem, a transaction error, or were the victim of fraud, it is important to understand the potential recovery routes. Marie can assist you in determining the specific actions you can take to attempt to regain your lost USDT when you need guidance and clarification. You can reach her via email at [email protected] and WhatsApp at +1 7127594675.
21.10.25 11:45 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
21.10.25 11:45 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
22.10.25 04:48 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
22.10.25 07:36 donnacollier

HOW I RECOVERED MY BITCOIN FROM CRYPTO INVESTMENT SCAM HOW I RECOVERED MY BITCOIN FROM CRYPTO INVESTMENT SCAM Hello everyone l’m by name Donna collier I live in urbandale 3 weeks ago was the darkest days of my life, i invested my hard earned money the sum of $123,000 into a crypto currency platform I was introduced to by a friend I met online everything happen so fast I was promised 300% of return of investment when it was time for me to cash out my investment and profit the platform was down I was so diversitated confused and tried to end it all then I came across upswing Ai a renowned expert in crypto currency and digital assets recovery at first it seem impossible after taking up my case within the the next 48 hours they where able to track down those fraud stars and recover my money I can’t recommend them enough to any one facing likewise change I will recommend you contact upswing Ai on Contact Details: WhatsApp +,1,2,0,2,8,1,0,1,4,0,7 E m a i l @Upswing-ai.com Website https: // u psw ing-ai. com/ platform /
22.10.25 11:59 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
22.10.25 11:59 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
22.10.25 16:31 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
23.10.25 01:52 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
23.10.25 01:52 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
23.10.25 15:47 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
23.10.25 21:43 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
23.10.25 21:43 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
24.10.25 06:08 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
24.10.25 06:40 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
24.10.25 06:40 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
24.10.25 06:54 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
24.10.25 18:18 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
24.10.25 18:18 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
25.10.25 00:49 tyleradams

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25.10.25 00:50 stevekalfman

If you ever need hacking services, look no further. I found myself in a difficult situation after losing almost $510,000 USD in bitcoin. I was distraught and had no hope of survival because i lost my life savings to this scam, I had no chance of recovering my investment. Until i came across an article on google about ([email protected]). A real-life recovery expert, everything changed completely after contacting him and explaining my ordeal to him and he quickly stepped in and assisted me in recovering 95% of my lost funds. They guarantee their clients and i got the highest level of happiness their services are highly recommended. so I’m putting this here for anyone who require their services too" Email: [email protected]
25.10.25 05:05 victoriabenny463

A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)
25.10.25 10:13 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
25.10.25 10:13 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
26.10.25 01:03 Christopherbelle

A terrible financial shock hit me hard. I lost $860,000 in a fake crypto scheme. Things looked good until I tried to cash out my earnings. Suddenly, my account vanished into thin air. I told the police many times, but help never showed up. Despair washed over me; I felt totally beaten. Then, I found Sylvester Bryant Intelligence. Right away, they were skilled and honest about the whole thing. They looked deep into my situation. They tracked where the stolen funds went. They fought hard for me every step of the way. To my great surprise, they got my money back. I thought that was impossible. I owe them so much for their hard work and truthfulness. Sylvester Bryant Intelligence restored my peace. If scams took your crypto, contact them now. Contact Info: Yt7cracker@gmail . com WhatsApp: ‪+1 512 577 7957. or +44 7428 662701.
26.10.25 18:09 victoriabenny463

A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)
27.10.25 11:15 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.10.25 11:15 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.10.25 17:08 raymondgonzales

Three Cheers for Wizard Hilton Cyber Tech, Bitcoin Savior Extraordinaire In the ever-evolving world of cryptocurrency, where volatility and uncertainty reign supreme, one individual has emerged as a beacon of hope and innovation - Wizard Hilton Cyber Tech, the self-proclaimed "Bitcoin Savior Extraordinaire." This enigmatic figure, with his uncanny ability to navigate the complexities of the digital asset landscape, has captivated the attention of crypto enthusiasts and skeptics alike. Wizard Hilton Cyber Tech journey began as a humble programmer, tinkering with the underlying blockchain technology that powers Bitcoin. But it was his visionary approach and unwavering commitment to the cryptocurrency's potential that propelled him into the limelight. Through a series of strategic investments, groundbreaking algorithmic trading strategies, and a knack for anticipating market shifts, Wizard Hilton Cyber Tech has managed to consistently outperform even the savviest of Wall Street traders. Wizard Hilton Cyber Tech ability to turn even the most tumultuous of Bitcoin price swings into opportunities for substantial gains has earned him the moniker "Wizard," a testament to his unparalleled mastery of the digital currency realm. But Wizard Hilton Cyber Tech impact extends far beyond personal wealth accumulation - Wizard Hilton Cyber Tech has tirelessly advocated for the widespread adoption of Bitcoin, working tirelessly to educate the public, lobby policymakers, and collaborate with industry leaders to overcome the barriers that have long hindered the cryptocurrency's mainstream acceptance. With infectious enthusiasm and boundless energy, Wizard Hilton Cyber Tech has become a true champion of the Bitcoin cause, inspiring a new generation of crypto enthusiasts to embrace the transformative power of this revolutionary technology. As the digital currency landscape continues to evolve, Wizard Hilton Cyber Tech name will undoubtedly be etched in the annals of cryptocurrency history as a visionary, a trailblazer, and, above all, the Bitcoin Savior Extraordinaire. To get your stolen bitcoin back, reach out to Wizard Hilton Cyber Tech via: Email : wizardhiltoncybertech ( @ ) gmail (. ) com WhatsApp number +18737715701 Good Day.
27.10.25 17:20 fatimanorth

The Federal Trade Commission said that more than $1 billion had been lost to cryptocurrency scams in 2023. Victims frequently lose everything, including hope, trust, and wealth. When your hard-earned money disappears into digital shadows, you feel trapped. Nowadays, cryptocurrency frauds are very common. You can get help from recovery specialist Marie at [email protected] and via WhatsApp at +1 7127594675.
28.10.25 00:55 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.10.25 00:55 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
29.10.25 03:43 Christopherbelle

A sudden money crisis struck me. I dropped $82,000 to a phony crypto scam. All seemed fine until I went to pull out my gains. Then, i was unable to get back my hard earned money. I reported it to the police several times. No aid came my way. Deep sadness hit me; I felt crushed. That's when I learned about Sylvester Bryant Intelligence. They acted quick and fair from the start. They checked my case closely. They followed the path of my lost cash. They pushed strong for me at each turn. In shock, they brought my funds back. I had figured it could not happen. I thank them for their effort and honesty. Sylvester Bryant Intelligence gave me calm again. If a scam stole your crypto, reach out to them today. Contact Info: Yt7cracker@gmail . com WhatsApp: +1 512 577 7957 or +44 7428 662701.
29.10.25 10:56 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
29.10.25 10:56 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
30.10.25 09:49 Christopherbelle

I suffered a huge money blow when $80,000 slipped away in a bogus crypto plot. It all looked great at first. Then I went to pull out my gains, and poof—my account was gone. I kept telling the cops about it, but they did zip. I felt shattered and lost. That's when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed clear steps, sharp know-how, and real drive to fix it. They tracked my missing cash step by step and pushed hard till they got it back. I swear, I figured it was a lost cause. Their straight-up work and trust brought back my calm. If a scam stole your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701
30.10.25 12:03 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