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# Untitled

a guest Apr 25th, 2019 69 Never
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1. import numpy as np
2.
3. def least_square_estimator(X, Y, method = None):
4.     """
5.     Compute beta (minimum cost computation)
6.     --------------------------
7.     (((X^T)X)^-1)((X^T)Y)
8.     --------------------------
9.     X : ndarray, shape(m_number, n_features)
10.
11.     Y : ndarray, shape(m_number, )
12.     """
13.     if method is 'QR':
14.         """
15.         ((R^-1)((Q^T)Y)
16.         """
17.         R = np.linalg.qr(X)[1]
18.         return np.dot(np.linalg.inv(R), np.dot(Q.T, Y))
19.
20.     elif method is 'Cholesky':
21.         """
22.         ((L(L^T))^-1)((X^T)Y)
23.         """
24.         L = np.linalg.cholesky(np.dot(X.T, X))
25.         return np.dot(np.linalg.inv(np.dot(L, L.T)), np.dot(X.T, Y))
26.
27.     elif method is 'SVD':
28.         """
29.         (V(D^-1))((U^T)Y)
30.         """
31.         u, s, vh = np.linalg.svd(X, full_matrices = True)
32.         d = np.diag(s)
33.         u = u[:, :d.shape[0]]
34.         return np.dot(np.dot(np.dot(vh.T, np.linalg.inv(d)), u.T), Y)
35.     return np.dot(np.linalg.inv(np.dot(X.T, X)), np.dot(X.T, Y))
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