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ML/algorithms/linearregression/linear_regression_gradient_descent.py

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+"""
+Implementation of Linear Regression using Gradient Descent.
+
+Let m = #training examples, n = #number of features Sizes differ 
+a little bit from blog notation. It takes as input the following: 
+y is R^(1 x m), X is R^(n x m), w is R^(n x 1)
+
+Programmed by Aladdin Persson <aladdin.persson at hotmail dot com>
+*    2020-04-03 Initial coding
+*    2020-04-25 Updated comments, and small changes in code
+"""
+
+import numpy as np
+
+
+class LinearRegression:
+    def __init__(self, print_cost=False):
+        self.learning_rate = 0.01
+        self.total_iterations = 1000
+        self.print_cost = print_cost
+
+    def y_hat(self, X, w):
+        return np.dot(w.T, X)
+
+    def cost(self, yhat, y):
+        C = 1 / self.m * np.sum(np.power(yhat - y, 2))
+
+        return C
+
+    def gradient_descent(self, w, X, y, yhat):
+        dCdW = 2 / self.m * np.dot(X, (yhat - y).T)
+        w = w - self.learning_rate * dCdW
+
+        return w
+
+    def main(self, X, y):
+        # Add x1 = 1
+        ones = np.ones((1, X.shape[1]))
+        X = np.append(ones, X, axis=0)
+
+        self.m = X.shape[1]
+        self.n = X.shape[0]
+
+        w = np.zeros((self.n, 1))
+
+        for it in range(self.total_iterations + 1):
+            yhat = self.y_hat(X, w)
+            cost = self.cost(yhat, y)
+
+            if it % 2000 == 0 and self.print_cost:
+                print(f"Cost at iteration {it} is {cost}")
+
+            w = self.gradient_descent(w, X, y, yhat)
+
+        return w
+
+
+if __name__ == "__main__":
+    X = np.random.rand(1, 500)
+    y = 3 * X + 5 + np.random.randn(1, 500) * 0.1
+    regression = LinearRegression()
+    w = regression.main(X, y)