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# nyk510/bias_variance.py

Created November 10, 2019 10:43
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PRML Section3 Figure3.5
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 import numpy as np import matplotlib.pyplot as plt def gaussian_kernel(x, basis=None): if basis is None: basis = np.linspace(-1.2, 1.2, 101) # parameter is my choice >_< phi = np.exp(- (x.reshape(-1, 1) - basis) ** 2 * 250) # add bias basis phi = np.hstack([phi, np.ones_like(phi[:, 0]).reshape(-1, 1)]) return phi def estimate_ml_weight(x, t, lam, xx): basis = np.linspace(0, 1, 24) phi = gaussian_kernel(x, basis=basis) w_ml = np.linalg.inv(phi.T.dot(phi) + lam * np.eye(len(basis) + 1)).dot(phi.T).dot(t) xx_phi = gaussian_kernel(xx, basis=basis) pred = xx_phi.dot(w_ml) return pred n_samples = 100 fig, axes = plt.subplots(ncols=2, nrows=3, figsize=(10, 12), sharey=True, sharex=True) for i, l in enumerate([2.6, -.31, -2.4]): ax = axes[i] preds = [] for n in range(n_samples): x = np.random.uniform(0, 1, 40) xx = np.linspace(0, 1, 101) t = np.sin(x * 2 * np.pi) + .2 * np.random.normal(size=len(x)) pred = estimate_ml_weight(x, t, lam=np.exp(l), xx=xx) if n < 20: ax[0].plot(xx, pred, c='black', alpha=.8, linewidth=1) preds.append(pred) ax[1].plot(xx, np.sin(2 * xx * np.pi), c='black', label=f'Lambda = {l}') ax[1].plot(xx, np.mean(preds, axis=0), '--', c='black') ax[1].legend() fig.tight_layout() fig.savefig('bias_variance.png', dpi=120)