def main():
# Generate training data
N = 25
f = lambda x: np.sin(2 * np.pi * x).flatten()
sigma = 0.2
sample = RegressionSample(f, N, sigma=sigma)
x = sample.x
t = sample.t
# Geenerate test data
x_min, x_max = x.min(), x.max()
t_min, t_max = t.min(), t.max()
x_test = np.array([np.linspace(x_min, x_max, 200)]).T
t_test = f(x_test)
# Construct basis functions
basis_functions = []
locs = np.linspace(x.min(), x.max(), 9)
for loc in locs:
basis = (
lambda loc: (lambda x: np.e**(-(linalg.norm(x - loc)**2) / (2 * 1e-2)))
)(loc)
basis_functions.append(basis)
n_basis = len(basis_functions)
# Model fitting
alpha = 2.0
prior_cov = np.eye(n_basis) / alpha
prior_mean = np.zeros(n_basis)
blr = BayesianLinearRegression(basis_functions=basis_functions,
mean=prior_mean,
cov=prior_cov)
# Sequential learning
beta = (1 / sigma)**2
subplot_list = [0, 1, 3, 24]
fig_row = 2
fig_col = np.ceil(len(subplot_list) / fig_row)
fig_no = 0
for i in range(N):
blr.fit(x[i, :], t[i], beta)
if (all(np.in1d(i, subplot_list))):
# Prediction
pred_mean, pred_cov = blr.predict(x_test, beta)
plt.figure(1)
plt.subplot(fig_row, fig_col, fig_no + 1)
plt.scatter(x[0:subplot_list[fig_no] + 1, :],
t[0:subplot_list[fig_no] + 1],
marker='x',
zorder=20)
plt.plot(x_test[:, 0], t_test, 'r-', zorder=10)
plt.plot(x_test[:, 0], pred_mean, 'g-', zorder=10)
color = np.array(['w', 'r'])
cmap = ListedColormap(['#FFFFFF', '#FFAAAA'])
h = 0.05
xx, yy = np.meshgrid(
np.arange(x_min, x_max, h), np.arange(t_min, t_max, h))
mesh = np.c_[xx.ravel(), yy.ravel()]
mesh_pred_mean, mesh_pred_cov = blr.predict(np.c_[mesh[:, 0]],
beta)
mesh_pred_std = np.sqrt(mesh_pred_cov)
upper = mesh_pred_mean + mesh_pred_std
lower = mesh_pred_mean - mesh_pred_std
inbound = np.array(
(mesh[:, 1] > lower) * (mesh[:, 1] < upper),
dtype=int).reshape(xx.shape)
plt.pcolormesh(xx, yy, inbound, cmap=cmap)
# Sample on w
plt.figure(2)
plt.subplot(fig_row, fig_col, fig_no + 1)
plt.scatter(x[0:subplot_list[fig_no] + 1, :],
t[0:subplot_list[fig_no] + 1],
marker='x',
zorder=20)
plt.plot(x_test[:, 0], pred_mean, 'g-', zorder=10)
w_sample = np.array(np.random.multivariate_normal(blr.mean, blr.cov, size=5))
for w in w_sample:
Phi = blr.nonlinear_transformation(x_test)
y = w.dot(Phi.T).flatten()
plt.plot(x_test[:, 0], y, 'r-', zorder=10)
fig_no += 1
plt.show()