import numpy as np import pandas as pd class RidgeRegression: def __init__( self, alpha: float = 0.001, lambda_: float = 0.1, iterations: int = 1000 ) -> None: """ Ridge Regression Constructor :param alpha: Learning rate for gradient descent :param lambda_: Regularization parameter (L2 regularization) :param iterations: Number of iterations for gradient descent """ self.alpha = alpha self.lambda_ = lambda_ self.iterations = iterations self.theta = None def feature_scaling( self, features: np.ndarray ) -> tuple[np.ndarray, np.ndarray, np.ndarray]: """ Normalize features to have mean 0 and standard deviation 1. :param features: Input features, shape (m, n) :return: Tuple containing: - Scaled features - Mean of each feature - Standard deviation of each feature Example: >>> rr = RidgeRegression() >>> features = np.array([[1, 2], [2, 3], [4, 6]]) >>> scaled_features, mean, std = rr.feature_scaling(features) >>> np.allclose(scaled_features.mean(axis=0), 0) True >>> np.allclose(scaled_features.std(axis=0), 1) True """ mean = np.mean(features, axis=0) std = np.std(features, axis=0) # Avoid division by zero for constant features (std = 0) std[std == 0] = 1 # Set std=1 for constant features to avoid NaN scaled_features = (features - mean) / std return scaled_features, mean, std def fit(self, x: np.ndarray, y: np.ndarray) -> None: """ Fit the Ridge Regression model to the training data. :param x: Input features, shape (m, n) :param y: Target values, shape (m,) """ x_scaled, mean, std = self.feature_scaling(x) # Normalize features m, n = x_scaled.shape self.theta = np.zeros(n) # Initialize weights to zeros for _ in range(self.iterations): predictions = x_scaled.dot(self.theta) error = predictions - y # Compute gradient with L2 regularization gradient = (x_scaled.T.dot(error) + self.lambda_ * self.theta) / m self.theta -= self.alpha * gradient # Update weights def predict(self, x: np.ndarray) -> np.ndarray: """ Predict values using the trained model. :param x: Input features, shape (m, n) :return: Predicted values, shape (m,) """ x_scaled, _, _ = self.feature_scaling(x) # Scale features using training data return x_scaled.dot(self.theta) def compute_cost(self, x: np.ndarray, y: np.ndarray) -> float: """ Compute the cost function with regularization. :param x: Input features, shape (m, n) :param y: Target values, shape (m,) :return: Computed cost """ x_scaled, _, _ = self.feature_scaling(x) # Scale features using training data m = len(y) predictions = x_scaled.dot(self.theta) cost = (1 / (2 * m)) * np.sum((predictions - y) ** 2) + ( self.lambda_ / (2 * m) ) * np.sum(self.theta**2) return cost def mean_absolute_error(self, y_true: np.ndarray, y_pred: np.ndarray) -> float: """ Compute Mean Absolute Error (MAE) between true and predicted values. :param y_true: Actual target values, shape (m,) :param y_pred: Predicted target values, shape (m,) :return: MAE """ return np.mean(np.abs(y_true - y_pred)) # Example usage if __name__ == "__main__": # Load dataset data = pd.read_csv( "https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/master/Week1/ADRvsRating.csv" ) x = data[["Rating"]].to_numpy() # Feature: Rating y = data["ADR"].to_numpy() # Target: ADR y = (y - np.mean(y)) / np.std(y) # Add bias term (intercept) to the feature matrix x = np.c_[np.ones(X.shape[0]), x] # Add intercept term # Initialize and train the Ridge Regression model model = RidgeRegression(alpha=0.01, lambda_=0.1, iterations=1000) model.fit(x, y) # Predictions predictions = model.predict(x) # Results print("Optimized Weights:", model.theta) print("Cost:", model.compute_cost(x, y)) print("Mean Absolute Error:", model.mean_absolute_error(y, predictions))