📝 : added comment to 5.3.

Author: Kariusdi

Regularization/scratching/5.3_vectorized.py

@@ -12,32 +12,40 @@ def define_X_include_bias(X):
 def problem(X):
     return np.sin(np.dot(np.pi, X))
 
+# Define a mean model calculation
 def meanModel(models):
     return np.mean(models, axis=0)
 
+# Define a bias calculation
 def computeBias(mean_model):
     z = np.square(mean_model - y)
     return np.mean(z)
 
+# Define a variance calculation
 def computeVariance(E_d, mean_model):
     z = np.square(E_d - mean_model)
     var_x = np.mean(z)
     return np.mean(var_x)
 
+# Define a E out calculation
 def computeEout(bias, variance):
     return bias + variance
 
 if __name__ == "__main__":
-    # Generate X features
+    
+    # Generate X from -1 to 1 with a hundred values
     X = np.linspace(-1, 1, 100)
-    # Compute y values
+    
+    # Make y values from problem function (sin)
     y = problem(X)
 
-    # Define X data (bias + weigths)
+    # Add bias term to X at the first column
     X_b = define_X_include_bias(X)
 
+    # For collecting prediction value of each genaral data for both models
     E_d_linear = []
     E_d_ridge = []
+    
     # Initialize subplots
     fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 6))
 
@@ -56,26 +64,34 @@ def computeEout(bias, variance):
 
     # Perform the training and plotting in the loop
     for _ in range(1000):
+        # Create Linear model
         linearModel = LinearRegression()
+        # Create Ridge model
         ridgeModel = RidgeRegression(lambda_param=0.5)
 
         # Randomly select 2 values from the dataset
         rands_X = np.random.choice(X, 2)
-        y_sample = problem(rands_X)
+        
+        # Create X and y from genaral value for training
         X_sample = define_X_include_bias(rands_X)
+        y_sample = problem(rands_X)
 
+        # Train model to fit the data with normal equation
         linearModel.training(X=X_sample, y=y_sample, type="normalEq")
         ridgeModel.training(X=X_sample, y=y_sample, type="normalEq")
 
+        # Make a prediction with the model that train only 2 data but use with all data for both models
         y_pred_lin = linearModel.prediction(X_b)
         E_d_linear.append(y_pred_lin)
 
         y_pred_ridge = ridgeModel.prediction(X_b)
         E_d_ridge.append(y_pred_ridge)
 
+        # Plot the prediction line for each iters with random genaral data
         ax1.plot(X, y_pred_lin, c="black", alpha=0.05)
         ax2.plot(X, y_pred_ridge, c="black", alpha=0.05)
 
+    # Calculate mean model, bias, varaince, and E out for both models to see the difference between non-regularization and regularization
     mean_linearModel = meanModel(E_d_linear)
     mean_ridgeModel = meanModel(E_d_ridge)
 
@@ -100,9 +116,9 @@ def computeEout(bias, variance):
     ax1.set_title(f'Linear Regression \n Bias = {bias_linearModel:.2f} | Varinace = {variance_linearModel:.2f} | E out = {eOut_linearModel:.2f}')
     ax2.set_title(f'Ridge Regression \n Bias = {bias_ridgeModel:.2f} | Varinace = {variance_ridgeModel:.2f} | E out = {eOut_ridgeModel:.2f}')
 
+    # Plot the mean predictions line
     ax1.plot(X, mean_linearModel, c="red", label="Mean Model", linewidth=2)
     ax2.plot(X, mean_ridgeModel, c="red", label="Mean Model", linewidth=2)
 
-    # Display the plots
     plt.tight_layout()
     plt.show()