Updated code as per PR feedback 2

Author: prajwal-38

machine_learning/ridge_regression.py

@@ -2,16 +2,9 @@
 from matplotlib import pyplot as plt
 from sklearn import datasets
 
-
 # Ridge Regression function
 # reference : https://en.wikipedia.org/wiki/Ridge_regression
-<<<<<<< HEAD
 def ridge_cost_function(x: np.ndarray, y: np.ndarray, theta: np.ndarray, alpha: float) -> float:
-=======
-def ridge_cost_function(
-    X: np.ndarray, y: np.ndarray, theta: np.ndarray, alpha: float
-) -> float:
->>>>>>> a4f585c89d4426f2ddace3ead610ff1742922713
     """
     Compute the Ridge regression cost function with L2 regularization.
 
@@ -33,28 +26,11 @@ def ridge_cost_function(
     """
     m = len(y)
     predictions = np.dot(X, theta)
-<<<<<<< HEAD
     cost = (1 / (2 * m)) * np.sum((predictions - y) ** 2)
     cost += (alpha / 2) * np.sum(theta[1:] ** 2)
     return cost
 
 def ridge_gradient_descent(x: np.ndarray, y: np.ndarray, theta: np.ndarray, alpha: float, learning_rate: float, max_iterations: int) -> np.ndarray:
-=======
-    cost = (1 / (2 * m)) * np.sum((predictions - y) ** 2) + (alpha / 2) * np.sum(
-        theta[1:] ** 2
-    )
-    return cost
-
-
-def ridge_gradient_descent(
-    X: np.ndarray,
-    y: np.ndarray,
-    theta: np.ndarray,
-    alpha: float,
-    learning_rate: float,
-    max_iterations: int,
-) -> np.ndarray:
->>>>>>> a4f585c89d4426f2ddace3ead610ff1742922713
     """
     Perform gradient descent to minimize the cost function and fit the Ridge regression model.
 
@@ -85,6 +61,7 @@ def ridge_gradient_descent(
     return theta
 
 
+
 if __name__ == "__main__":
     import doctest
     doctest.testmod()
@@ -106,24 +83,20 @@ def ridge_gradient_descent(
     learning_rate = 0.01
     max_iterations = 1000
 
-    optimized_theta = ridge_gradient_descent(
-        X, y, theta_initial, alpha, learning_rate, max_iterations
-    )
+    optimized_theta = ridge_gradient_descent(X, y, theta_initial, alpha, learning_rate, max_iterations)
     print(f"Optimized theta: {optimized_theta}")
 
     # Prediction
     def predict(X, theta):
         return np.dot(X, theta)
-
     y_pred = predict(X, optimized_theta)
 
     # Plotting the results (here we visualize predicted vs actual values)
     plt.figure(figsize=(10, 6))
-    plt.scatter(y, y_pred, color="b", label="Predictions vs Actual")
-    plt.plot([min(y), max(y)], [min(y), max(y)], color="r", label="Perfect Fit")
+    plt.scatter(y, y_pred, color='b', label='Predictions vs Actual')
+    plt.plot([min(y), max(y)], [min(y), max(y)], color='r', label='Perfect Fit')
     plt.xlabel("Actual values")
     plt.ylabel("Predicted values")
     plt.title("Ridge Regression: Actual vs Predicted Values")
     plt.legend()
-    #plots on a graph
     plt.show()