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