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## Implement Ridge Regression Loss Function

#### Example

## Ridge Regression Loss

### Key Concepts:

### Ridge Loss Function:

### Implementation Steps:

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: 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) # Expected Output: 2.204

Ridge Regression is a linear regression method with a regularization term to prevent overfitting by controlling the size of the coefficients.

**Regularization:**Adds a penalty to the loss function to discourage large coefficients, helping to generalize the model.**Mean Squared Error (MSE):**Measures the average squared difference between actual and predicted values.**Penalty Term:**The sum of the squared coefficients, scaled by the regularization parameter \( \lambda \), which controls the strength of the regularization.

The Ridge Loss function combines MSE and the penalty term:

\[ L(\beta) = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 + \lambda \sum_{j=1}^{p} \beta_j^2 \]

**Calculate MSE:**Compute the average squared difference between actual and predicted values.**Add Regularization Term:**Compute the sum of squared coefficients multiplied by \( \lambda \).**Combine and Minimize:**Sum MSE and the regularization term to form the Ridge loss, then minimize this loss to find the optimal coefficients.

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

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