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