import numpy as np import pandas as pd class RidgeRegression: def __init__(self, alpha=0.001, lambda_=0.1, iterations=1000): """ 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, X): """ Normalize features to have mean 0 and standard deviation 1 :param X: Input features, shape (m, n) :return: Scaled features, mean, and std for each feature """ mean = np.mean(X, axis=0) std = np.std(X, axis=0) # Avoid division by zero for constant features (std = 0) std[std == 0] = 1 # Set std=1 for constant features to avoid NaN X_scaled = (X - mean) / std return X_scaled, mean, std def fit(self, X, y): """ 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 i 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): """ 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, y): """ 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, y_pred): """ 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 df = pd.read_csv( "https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/master/Week1/ADRvsRating.csv" ) X = df[["Rating"]].values # Feature: Rating y = df["ADR"].values # 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))