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November 27, 2017 11:53
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| import numpy as np | |
| import matplotlib.pyplot as plt | |
| n = 50 | |
| Xtest = np.linspace(-5, 5, n).reshape(-1,1) | |
| def kernel(a, b, param): | |
| sqdist = np.sum(a**2, 1).reshape(-1,1) + np.sum(b**2, 1) - 2*np.dot(a, b.T) | |
| return np.exp(-0.5 * (1/param) * sqdist) | |
| param = 0.1 | |
| K_ss = kernel(Xtest, Xtest, param) | |
| L = np.linalg.cholesky(K_ss + 1e-15*np.eye(n)) | |
| f_prior = np.dot(L, np.random.normal(size=(n,3))) | |
| # plt.plot(Xtest, f_prior) | |
| # plt.title('Three samples from the GP prior') | |
| # plt.grid() | |
| # plt.xlim([-5, 5]) | |
| # plt.show() | |
| Xtrain = np.array([-4, -3, -2, -1, 1]).reshape(5, 1) | |
| ytrain = np.sin(Xtrain) | |
| K = kernel(Xtrain, Xtrain, param) | |
| L = np.linalg.cholesky(K + 0.00005*np.eye(len(Xtrain))) | |
| K_s = kernel(Xtrain, Xtest, param) | |
| Lk = np.linalg.solve(L, K_s) | |
| mu = np.dot(Lk.T, np.linalg.solve(L, ytrain)).reshape((n,)) | |
| s2 = np.diag(K_ss) - np.sum(Lk**2, axis=0) | |
| stdv = np.sqrt(s2) | |
| L = np.linalg.cholesky(K_ss + 1e-6*np.eye(n) - np.dot(Lk.T, Lk)) | |
| f_post = mu.reshape(-1,1) + np.dot(L, np.random.normal(size=(n,3))) | |
| plt.plot(Xtrain, ytrain, 'bs', ms=8) | |
| plt.plot(Xtest, f_post) | |
| plt.gca().fill_between(Xtest.flat, mu-2*stdv, mu+2*stdv, color="#dddddd") | |
| plt.plot(Xtest, mu, 'r--', lw=2) | |
| # pl.axis([-5, 5, -3, 3]) | |
| plt.title('Three samples from the GP posterior') | |
| plt.show() |
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