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ML/algorithms/linearregression/linear_regression_normal_equation.py

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+"""
+Implementation of Linear Regression using the Normal Equation.
+
+Let m = #training examples, n = #number of features and the
+input shapes are y is R^(m x 1), X is R^(m x n), w is R^(n x 1).
+Using these shapes, the normal equation implementation is
+exactly as the derived formula :) 
+
+Programmed by Aladdin Persson <aladdin.persson at hotmail dot com>
+*    2020-04-25 Initial coding
+"""
+
+import numpy as np
+
+
+def linear_regression_normal_equation(X, y):
+    ones = np.ones((X.shape[0], 1))
+    X = np.append(ones, X, axis=1)
+    W = np.dot(np.linalg.pinv(np.dot(X.T, X)), np.dot(X.T, y))
+    return W
+
+
+if __name__ == "__main__":
+    # Run a small test example: y = 5x (approximately)
+    m, n = 500, 1
+    X = np.random.rand(m, n)
+    y = 5 * X + np.random.randn(m, n) * 0.1
+    W = linear_regression_normal_equation(X, y)