Implement Ridge Regression Loss Function

Implement Ridge Regression Loss Function

Write a Python function ridge_loss that implements the Ridge Regression loss function. The function should take a 2D numpy array X representing the feature matrix, a 1D numpy array w representing the coefficients, a 1D numpy array y_true representing the true labels, and a float alpha representing the regularization parameter. The function should return the Ridge loss, which combines the Mean Squared Error (MSE) and a regularization term.

Example:

Input:

import numpy as np

X = np.array([[1, 1], [2, 1], [3, 1], [4, 1]])
w = np.array([0.2, 2])
y_true = np.array([2, 3, 4, 5])
alpha = 0.1

loss = ridge_loss(X, w, y_true, alpha)
print(loss)

Output:

2.204

Reasoning:

The Ridge loss is calculated using the Mean Squared Error (MSE) and a regularization term. The output represents the combined loss value.

import numpy as np

def ridge_loss(X: np.ndarray, w: np.ndarray, y_true: np.ndarray, alpha: float) -> float:
	# Your code here
	pred = X.dot(w)
	l2 = alpha * np.sum(w ** 2)
	MSE = np.mean((pred - y_true) ** 2)
	ridge_MSE = MSE + l2
	return ridge_MSE

Test Case Results

2 of 2 tests passed

官方题解

import numpy as np

def ridge_loss(X: np.ndarray, w: np.ndarray, y_true: np.ndarray, alpha: float) -> float:
    loss = np.mean((y_true - X @ w)**2) + alpha * np.sum(w**2)
    return loss