enhancement

machine_learning/01_linear_regression.py

@@ -0,0 +1,57 @@
+import numpy as np
+
+
+# -------------------- Naive Linear Regression --------------------
+def naive_linear_regression(X, y, learning_rate=0.01, epochs=1000):
+    """
+    Naive Linear Regression using loops.
+    X: input features (2D array)
+    y: target values (column vector)
+    """
+    m, n = X.shape
+    theta = np.zeros((n, 1))  # initialize parameters
+
+    for _ in range(epochs):
+        predictions = []
+        for i in range(m):
+            pred = 0
+            for j in range(n):
+                pred += X[i][j] * theta[j][0]
+            predictions.append([pred])
+        predictions = np.array(predictions)
+        # compute gradient
+        errors = predictions - y
+        for j in range(n):
+            grad = 0
+            for i in range(m):
+                grad += errors[i][0] * X[i][j]
+            theta[j][0] -= learning_rate * grad / m
+    return theta
+
+
+# -------------------- Vectorized Linear Regression --------------------
+def vectorized_linear_regression(X, y, learning_rate=0.01, epochs=1000):
+    """
+    Fully vectorized Linear Regression using matrix operations.
+    """
+    m, n = X.shape
+    theta = np.zeros((n, 1))
+    for _ in range(epochs):
+        predictions = X.dot(theta)
+        errors = predictions - y
+        gradient = (X.T.dot(errors)) / m
+        theta -= learning_rate * gradient
+    return theta
+
+
+# -------------------- Test Both Implementations --------------------
+if __name__ == "__main__":
+    # Sample dataset
+    X = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])
+    y = np.dot(X, np.array([[1], [2]])) + 3  # y = 1*x1 + 2*x2 + 3
+
+    theta_naive = naive_linear_regression(X, y)
+    theta_vec = vectorized_linear_regression(X, y)
+
+    print("Theta naive:\n", theta_naive)
+    print("Theta vectorized:\n", theta_vec)