новая версия

ии2.py

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+import numpy as np
+from sklearn.linear_model import LinearRegression, SGDRegressor
+from sklearn.preprocessing import StandardScaler
+from sklearn.metrics import mean_squared_error
+
+# 1. Аналитическое решение
+def linear_regression_normal(X, y, add_intercept=True):
+    if y.ndim == 1:
+        y = y.reshape(-1, 1)
+    if add_intercept:
+        X = np.hstack([np.ones((X.shape[0], 1)), X])
+    w = np.linalg.pinv(X.T @ X) @ X.T @ y
+    return w.flatten()
+
+# 2. Полный градиентный спуск (SSE, без деления на n)
+def linear_regression_gd(X, y, lr=0.001, epochs=1000, add_intercept=True):
+    if y.ndim == 1:
+        y = y.reshape(-1, 1)
+    if add_intercept:
+        X = np.hstack([np.ones((X.shape[0], 1)), X])
+    w = np.zeros((X.shape[1], 1))
+    for _ in range(epochs):
+        error = X @ w - y
+        gradient = 2 * X.T @ error
+        w -= lr * gradient
+    return w.flatten()
+
+# 3. Стохастический градиентный спуск (с мини-батчами)
+def linear_regression_sgd(X, y, lr=0.01, epochs=100, batch_size=32, add_intercept=True):
+    if y.ndim == 1:
+        y = y.reshape(-1, 1)
+    if add_intercept:
+        X = np.hstack([np.ones((X.shape[0], 1)), X])
+    w = np.zeros((X.shape[1], 1))
+    n = X.shape[0]
+    for _ in range(epochs):
+        indices = np.random.permutation(n)
+        X_shuffled = X[indices]
+        y_shuffled = y[indices]
+        for i in range(0, n, batch_size):
+            X_batch = X_shuffled[i:i+batch_size]
+            y_batch = y_shuffled[i:i+batch_size]
+            error = X_batch @ w - y_batch
+            gradient = 2 * X_batch.T @ error
+            w -= lr * gradient
+    return w.flatten()
+
+# Генерация данных
+np.random.seed(42)
+n, d = 200, 5
+X = np.random.randn(n, d)
+true_w = np.array([1.5, -2.0, 0.8, 3.1, -1.2])
+y = X @ true_w + 0.2 * np.random.randn(n)
+
+# Обучение наших моделей (без свободного члена для простоты)
+w_normal = linear_regression_normal(X, y, add_intercept=False)
+w_gd = linear_regression_gd(X, y, lr=0.001, epochs=2000, add_intercept=False)
+w_sgd = linear_regression_sgd(X, y, lr=0.001, epochs=100, batch_size=32, add_intercept=False)
+
+# sklearn LinearRegression
+lr_sk = LinearRegression(fit_intercept=False).fit(X, y)
+w_sk = lr_sk.coef_
+
+# sklearn SGDRegressor (требует масштабирования)
+scaler = StandardScaler()
+X_scaled = scaler.fit_transform(X)
+sgd_sk = SGDRegressor(fit_intercept=False, max_iter=1000, tol=1e-3, eta0=0.01, learning_rate='constant', random_state=42)
+sgd_sk.fit(X_scaled, y)
+w_sgd_sk = sgd_sk.coef_
+
+# Сравнение
+print("Истинные веса:          ", true_w)
+print("Аналитика (наша):        ", w_normal)
+print("GD (наша):               ", w_gd)
+print("SGD (наша):              ", w_sgd)
+print("sklearn LinearRegression:", w_sk)
+print("sklearn SGDRegressor:    ", w_sgd_sk)
+
+# Оценка MSE на тех же данных
+y_pred_normal = X @ w_normal
+y_pred_gd = X @ w_gd
+y_pred_sgd = X @ w_sgd
+y_pred_sk = X @ w_sk
+y_pred_sgd_sk = X_scaled @ w_sgd_sk   # важно: X_scaled использовался для обучения
+
+print("\nMSE:")
+print(f"  Normal equation: {mean_squared_error(y, y_pred_normal):.6f}")
+print(f"  GD:              {mean_squared_error(y, y_pred_gd):.6f}")
+print(f"  SGD:             {mean_squared_error(y, y_pred_sgd):.6f}")
+print(f"  sklearn LR:      {mean_squared_error(y, y_pred_sk):.6f}")
+print(f"  sklearn SGD:     {mean_squared_error(y, y_pred_sgd_sk):.6f}")