Update linear_regression.py

Author: rutubhanderi

Diff for: machine_learning/linear_regression.py

@@ -1,117 +1,56 @@
-"""
-Linear regression is the most basic type of regression commonly used for
-predictive analysis. The idea is pretty simple: we have a dataset and we have
-features associated with it. Features should be chosen very cautiously
-as they determine how much our model will be able to make future predictions.
-We try to set the weight of these features, over many iterations, so that they best
-fit our dataset. In this particular code, I had used a CSGO dataset (ADR vs
-Rating). We try to best fit a line through dataset and estimate the parameters.
-"""
-
 import numpy as np
 import requests
 
-
 def collect_dataset():
-    """Collect dataset of CSGO
-    The dataset contains ADR vs Rating of a Player
-    :return : dataset obtained from the link, as matrix
-    """
+    """Collect dataset of CSGO (ADR vs Rating of a Player)"""
     response = requests.get(
-        "https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/"
-        "master/Week1/ADRvsRating.csv",
+        "https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/master/Week1/ADRvsRating.csv",
         timeout=10,
     )
-    lines = response.text.splitlines()
-    data = []
-    for item in lines:
-        item = item.split(",")
-        data.append(item)
-    data.pop(0)  # This is for removing the labels from the list
-    dataset = np.matrix(data)
-    return dataset
-
-
-def run_steep_gradient_descent(data_x, data_y, len_data, alpha, theta):
-    """Run steep gradient descent and updates the Feature vector accordingly_
-    :param data_x   : contains the dataset
-    :param data_y   : contains the output associated with each data-entry
-    :param len_data : length of the data_
-    :param alpha    : Learning rate of the model
-    :param theta    : Feature vector (weight's for our model)
-    ;param return    : Updated Feature's, using
-                       curr_features - alpha_ * gradient(w.r.t. feature)
-    """
-    n = len_data
-
-    prod = np.dot(theta, data_x.transpose())
-    prod -= data_y.transpose()
-    sum_grad = np.dot(prod, data_x)
-    theta = theta - (alpha / n) * sum_grad
-    return theta
-
+    data = np.loadtxt(response.text.splitlines()[1:], delimiter=",")  # Skip the header
+    return data
 
-def sum_of_square_error(data_x, data_y, len_data, theta):
-    """Return sum of square error for error calculation
-    :param data_x    : contains our dataset
-    :param data_y    : contains the output (result vector)
-    :param len_data  : len of the dataset
-    :param theta     : contains the feature vector
-    :return          : sum of square error computed from given feature's
-    """
-    prod = np.dot(theta, data_x.transpose())
-    prod -= data_y.transpose()
-    sum_elem = np.sum(np.square(prod))
-    error = sum_elem / (2 * len_data)
-    return error
+def normalize_features(data):
+    """Normalize feature values to have mean 0 and variance 1"""
+    means = np.mean(data[:, :-1], axis=0)
+    stds = np.std(data[:, :-1], axis=0)
+    data[:, :-1] = (data[:, :-1] - means) / stds
+    return data
 
-
-def run_linear_regression(data_x, data_y):
-    """Implement Linear regression over the dataset
-    :param data_x  : contains our dataset
-    :param data_y  : contains the output (result vector)
-    :return        : feature for line of best fit (Feature vector)
-    """
-    iterations = 100000
-    alpha = 0.0001550
-
-    no_features = data_x.shape[1]
-    len_data = data_x.shape[0] - 1
-
-    theta = np.zeros((1, no_features))
+def run_gradient_descent(data_x, data_y, alpha=0.01, iterations=1000, batch_size=32):
+    """Run gradient descent with mini-batch optimization"""
+    len_data, no_features = data_x.shape
+    theta = np.zeros(no_features)
 
     for i in range(iterations):
-        theta = run_steep_gradient_descent(data_x, data_y, len_data, alpha, theta)
-        error = sum_of_square_error(data_x, data_y, len_data, theta)
-        print(f"At Iteration {i + 1} - Error is {error:.5f}")
+        indices = np.random.choice(len_data, batch_size, replace=False)  # Randomly sample indices
+        x_batch = data_x[indices]
+        y_batch = data_y[indices]
+
+        predictions = x_batch @ theta  # Vectorized predictions
+        errors = predictions - y_batch
+        
+        gradient = (1 / batch_size) * (x_batch.T @ errors)  # Vectorized gradient
+        theta -= alpha * gradient  # Update theta
+        
+        if i % 100 == 0:  # Print error every 100 iterations
+            error = np.mean(errors ** 2)  # Mean Squared Error
+            print(f"Iteration {i}: MSE = {error:.5f}")
 
     return theta
 
-
-def mean_absolute_error(predicted_y, original_y):
-    """Return sum of square error for error calculation
-    :param predicted_y   : contains the output of prediction (result vector)
-    :param original_y    : contains values of expected outcome
-    :return          : mean absolute error computed from given feature's
-    """
-    total = sum(abs(y - predicted_y[i]) for i, y in enumerate(original_y))
-    return total / len(original_y)
-
-
 def main():
     """Driver function"""
     data = collect_dataset()
+    data = normalize_features(data)  # Normalize the features
 
     len_data = data.shape[0]
-    data_x = np.c_[np.ones(len_data), data[:, :-1]].astype(float)
-    data_y = data[:, -1].astype(float)
+    data_x = np.c_[np.ones(len_data), data[:, :-1]]  # Add bias term
+    data_y = data[:, -1]
 
-    theta = run_linear_regression(data_x, data_y)
-    len_result = theta.shape[1]
+    theta = run_gradient_descent(data_x, data_y)
     print("Resultant Feature vector : ")
-    for i in range(len_result):
-        print(f"{theta[0, i]:.5f}")
-
+    print(theta)
 
 if __name__ == "__main__":
     main()