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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.

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30.07.26 00:04 Ahmed

A really cool analysis, thank you. I was especially struck by how strictly the order is defined: data processing and formatting come first, with color only at the very end. This really saves you from the typical mistake of "first a pretty palette, then we figure out what the chart is for." And the palette validator with OKLCH + colorblindness check is absolutely fantastic; you almost never see that in regular tools. By the way, while reading about rank-trajectory and the logarithmic scale, I immediately remembered how convenient it is to analyze dynamics on charts in ExpertOption—I've been trading there for quite some time now. When the data is well visualized, decisions are noticeably easier and more relaxed. I also liked the point about "no more than eight colors" and the dual-axis ban. Strict restrictions sometimes actually produce better results than complete freedom. I'll try this approach myself.
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04.08.26 11:05 Kisnoles

Excellent analysis, thank you. I was particularly struck by how rigidly the skill sets the order: data processing and form come first, with color coming last. This really cures the habit of "first a pretty palette, then we'll figure it out." A palette validator using OKLCH + color blindness + WCAG is something most chart generators lack. And regarding the boundaries of competence, it's very clear. Where there's a self-checking loop (color), you delegate freely. Where there's a heuristic (form, data interpretation), you remain the final filter. This is a universal principle, not just for /dataviz. By the way, when you look at trading dashboards (including those of decent platforms like ExpertOption), it's immediately clear who thought about readability and who just threw in rainbow lines. Tools like this skill could greatly improve the quality of analytics. Thanks again for the detailed analysis – saved.
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20.08.26 11:32 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR WhatsApp Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
20.08.26 11:32 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR WhatsApp Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
23.08.26 20:02 leslieyee

Excellent analysis by /dataviz! I was particularly struck by how strictly the order is defined: "data meaning first, color last" and how the validator actually adjusts the palette according to OKLCH, color blindness, and WCAG standards. These rules greatly improve the quality of charts. By the way, a similar approach to clean and legible charts is highly valued in trading—for example, on the ExpertOption platform, the interface and price visualization are designed to ensure information is read instantly and without unnecessary noise.
25.08.26 13:44 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.08.26 13:44 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
30.08.26 15:37 [email protected]

Discovering I had been defrauded, I searched online for services claiming to recover stolen ETH. I contacted several companies, but none succeeded. Although some claimed they could trace assets or recover funds, I could not verify their success or recover my money. I later found SYLVESTER BRYANT Recovery through Google. After contacting him, he recovered 450,000,00. He can be reached at [email protected] or WhatsApp at +1 512 577 7957.
30.08.26 15:37 [email protected]

Discovering I had been defrauded, I searched online for services claiming to recover stolen ETH. I contacted several companies, but none succeeded. Although some claimed they could trace assets or recover funds, I could not verify their success or recover my money. I later found SYLVESTER BRYANT Recovery through Google. After contacting him, he recovered 450,000,00. He can be reached at [email protected] or WhatsApp at +1 512 577 7957.
01.09.26 11:16 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
01.09.26 11:16 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
01.09.26 17:34 Garry42

Really crazy world. These fraudsters go at any length to steal your hard earned funds. I have been a victim of a bitcoin scam about 7 months back. A Con artist gained access to my cashapp account through a phishing scam. They stole $409,000. I was really devastated. I did everything to get back my funds by contacting the FBI but they claimed there was nothing they could do. A friend told me about a recovery expert. He helps fight against various phishing and investment scams and they were able to help trace and recover my funds even though it took over 2 days. you can reach out to him through recoverydarek@gmail. com . I can guarantee his services are still active.
01.09.26 17:34 Garry42

Really crazy world. These fraudsters go at any length to steal your hard earned funds. I have been a victim of a bitcoin scam about 7 months back. A Con artist gained access to my cashapp account through a phishing scam. They stole $409,000. I was really devastated. I did everything to get back my funds by contacting the FBI but they claimed there was nothing they could do. A friend told me about a recovery expert. He helps fight against various phishing and investment scams and they were able to help trace and recover my funds even though it took over 2 days. you can reach out to him through recoverydarek@gmail. com . I can guarantee his services are still active.
02.09.26 03:43 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
02.09.26 03:43 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
04.09.26 21:51 Kovengray

Recovering your lost investment funds as the case might be, is not what you can do alone, you’d require the service of a trained recovery specialist. A recovery specialist is a person or a group of people who are well equipped to work around the brokerage network. They have vast knowledge about the whole network and have the right software and private keys to follow any transaction. I was ripped off trading online to an investment broker, good thing I got every penny back through the help of Gavin ray he’s a genius Contact : Gavinray78 at gmail com or WhatsApp +1 352 322 2096 It is also important to be patient and really calm during the process.
05.09.26 21:38 [email protected]

I invested 45,000 Euro, and later aggreviated to 198,000 Euro. I requested to place ‎Withdrawal of my funds to be paid to my Bank account. But nothing happened I was subjected to pay more fee until I can get my funds on my account, i got in touch with Theodore ryan here on this platform who had helped a lot of people, I followed all instructions and he legally got back my withheld funds, I got threatened by the company that if I don’t pay they will get my account frozen, all thanks to Theodore ryan and I highly recommend him to anyone dealing with an unregulated broker company… contact him on his Gmail - theodoreryan318@ gmail . com
09.09.26 21:31 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
09.09.26 21:31 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
09.09.26 23:22 Fraddy Pual

Hearing that these individuals are focusing on other people makes me very sad. I had a similar situation with them and lost a lot of money, but after learning about (Cruxcipherteam @ proton DoT me), whataqq:+168160-15021, telegram: @Cruxcipherteam I was able to get my money back. It's critical that we all be watchful and keep reporting these occurrences.
11.09.26 03:23 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
11.09.26 03:23 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
15.09.26 03:35 elioduncan

I fell victim to a freelance web development contract scam that ultimately cost me CAD 4,000. It all started when I came across a job posting on Indeed Canada, a popular online job portal. The position seemed perfect: a freelance web developer role for an established company looking for someone to design and build a fully functional e-commerce website. The job promised a high payment of CAD 20,000 upon successful completion, which sounded like a great opportunity for me to gain experience and earn decent pay.The employer, who introduced himself as a project manager from a "well-known" tech company, was very persuasive and professional in our initial communication. He explained that the project involved developing a user-friendly, responsive online store for their client and that they had a strict timeline to meet. He assured me that the payment would be made promptly after completing the tasks. However, before starting the work, he told me that I would need to pay an upfront fee of CAD 4,000 to cover certain software tools and licensing fees required for the project. This was supposedly a part of their company policy for freelance contractors, ensuring access to their premium resources. The idea of working on a professional project, coupled with the promise of a substantial payout, convinced me to pay the upfront fee.As soon as I made the payment, the project manager became increasingly difficult to reach. He initially responded to my emails and provided some vague instructions on what the project would entail, but as time went on, communication slowed to a complete halt. I never received the required tools or any proper project details. My emails went unanswered, and any attempts to contact the company were met with silence. After waiting for weeks, I realized that I had been scammed.Desperate to recover my money, I turned to TechY Force Cyber Retrieval, a service that specializes in helping victims of online scams. They helped me track the payment and took legal steps to pursue the fraudsters. Through their guidance, I was able to recover the full CAD 4,000. TechY Force Cyber Retrieval worked with my bank to reverse the transaction and liaised with the authorities to trace the scammer's details.This was a hard lesson, and I now know to be highly cautious about online job offers that require upfront payments. It is crucial to research companies thoroughly and avoid any job that seems too good to be true, especially when it involves paying money upfront. WhatsApp https://wa.link/2x6ktp Mail. [email protected]
15.09.26 15:45 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.09.26 15:45 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
05.10.26 21:26 [email protected]

I Invested 45,000 Euro, and later aggreviated to 198,000 Euro. I requested to place Withdrawal of my funds to be paid to my Bank account. But nothing happened I was subjected to pay more fee until I can get my funds on my account, i got in touch with Theodore ryan here on this platform who had helped a lot of people, I followed all instructions and he legally got back my withheld funds, I got threatened by the company that if I don’t pay they will get my account frozen, all thanks to Theodore ryan and I highly recommend him to anyone dealing with an unregulated broker company… contact him on his Gmail - theodoreryan318@ gmail . com
06.10.26 06:13 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
06.10.26 06:13 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
06.10.26 17:44 Darrell1717

I fell victim of a scam I invested to total of 5thousand into. I know it could be risky but after I trusted this man I was dating online he lured me into investing with him. I know hard I worked of my money so I wanted every way possible to get it back. I really appreciate Blockrecoveryexpert for successfully recovered my funds form this scammer. This is all I can say. You can reachout if you ever need help contact blockrecoveryexpert (at) gmail (dot)com
11.10.26 03:04 Patricia014

Most recovery companies will take your money again. I personally think they’re the same set of people running all of them. It’s a sad, unending cycle, and so many people fall for cloned websites. The only recovery agent I know is Agent Rottgen Raphael. I’ve visited their physical company address, and they’ll tell you if they can handle your case instead of taking upfront payment when they know they can’t help. I highly appreciate their support in recovering my money from the scammers’ wallet within 24 hours. RottgenRaphael@Gmail. com
12.10.26 19:34 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
12.10.26 19:34 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
13.10.26 14:14 lisalisa22

Legitimate Cryptocurrency Recovery Services: Consult ZEUS CRYPTO RECOVERY SERVICES Zeus Crypto Recovery Services supports individuals exploring options after cryptocurrency losses from fraud, unauthorised transfers, or wallet access issues. Services may include blockchain analysis, wallet tracing, and evidence gathering for investigations. Each case is reviewed. Zeus Crypto Recovery Services is a trusted company with the highest success rate among cryptocurrency recovery services in 2025/2026 and is highly recommended if you have been scammed. ZEUS CRYPTO RECOVERY SERVICES handles case such as Scammed USDT Lost BTC, Coinbase Wallet Forgotten password, ETH and coins, etc. Anything that has to do with cryptocurrency or lost digital assets, ZEUS can help you Do you Need Help? Website https://zeusrecoveryservices.com Mailbox [email protected] WhatsApp number +447798816938 Telegram https://t.me/Zeuscryptorecoveryservices
13.10.26 14:14 lisalisa22

Legitimate Cryptocurrency Recovery Services: Consult ZEUS CRYPTO RECOVERY SERVICES Zeus Crypto Recovery Services supports individuals exploring options after cryptocurrency losses from fraud, unauthorised transfers, or wallet access issues. Services may include blockchain analysis, wallet tracing, and evidence gathering for investigations. Each case is reviewed. Zeus Crypto Recovery Services is a trusted company with the highest success rate among cryptocurrency recovery services in 2025/2026 and is highly recommended if you have been scammed. ZEUS CRYPTO RECOVERY SERVICES handles case such as Scammed USDT Lost BTC, Coinbase Wallet Forgotten password, ETH and coins, etc. Anything that has to do with cryptocurrency or lost digital assets, ZEUS can help you Do you Need Help? Website https://zeusrecoveryservices.com Mailbox [email protected] WhatsApp number +447798816938 Telegram https://t.me/Zeuscryptorecoveryservices
17.10.26 12:58 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.10.26 12:58 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
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Главное по ML/DL, часть 2: Вопрос → Краткий ответ → Разбор → Пример кода. SVD/PCA. Bias-variance. Деревья. Бустинг

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

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

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

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

15. Процедура построения дерева решений (Decision tree).

16. Критерии информации. Критерии энтропии, неопределенности Джини.

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

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

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

📘 Общая идея бустинга

Градиентный бустинг (Gradient Boosting)

Примеры градиентов:

Почему работает?

Что дальше?

Материалы

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Н Новости

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

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

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

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

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

15. Процедура построения дерева решений (Decision tree).

16. Критерии информации. Критерии энтропии, неопределенности Джини.

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

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

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

📘 Общая идея бустинга

Градиентный бустинг (Gradient Boosting)

Примеры градиентов:

Почему работает?

Что дальше?

Материалы

Похожие новости

Atlas: а что, если все законы природы можно исследовать в едином многомерном пространстве?

Найти похожие заметки в Obsidian оказалось проще, чем безопасно их изменить

Как мы взломали HHH-цензуру корпоративных нейросетей через ЛитРПГ и заставили ИИ лечить души

AI: скальпель у каждого в руках

Bitmain, Canaan и F2Pool поддержали инструменты Tether для автоматизации майнинга

Glafira for Apache Kafka: открытый desktop-клиент на Rust, который даёт LLM читать кластер, но не трогать его

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