def main():
# Generate training data
N = 10
f = [lambda x: np.sin(2 * np.pi * x).flatten(),
lambda x: np.cos(2 * np.pi * x).flatten()]
sample = RegressionSample(f, N, sigma=0.2)
x = sample.x
t = sample.t
# Generate 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 = np.array([fun(x_test) for fun in f]).T
# Construct basis functions
basis_functions = []
locs = np.linspace(-1, 1, 10)
for loc in locs:
basis = (lambda loc: (lambda x: np.e**(-0.5*linalg.norm(x - loc)**2)))(loc)
basis_functions.append(basis)
# Model fitting
lls = LinearLeastSquare(basis_functions=basis_functions)
lls.fit(x, t)
# Prediction
predictions = lls.predict(x_test)
std = np.sqrt(1 / lls.beta)
plt.figure()
fig_col = 2
fig_row = np.ceil(len(f) / fig_col)
for i, f in enumerate(f):
plt.subplot(fig_row, fig_col, i + 1)
plt.scatter(x, t[:, i], marker='x')
plt.plot(x_test[:, 0], t_test[:, i], 'r-')
plt.plot(x_test[:, 0], predictions[:, i], 'g-')
plt.plot(x_test[:, 0], predictions[:, i] + std, 'g--')
plt.plot(x_test[:, 0], predictions[:, i] - std, 'g--')
plt.title('The ${0}$th component of output'.format(i))
plt.show()
def main():
# Generate training data
N = 10
f = lambda x: np.sin(2 * np.pi * x).flatten()
sample = RegressionSample(f, N, sigma=0.2)
x = sample.x
t = sample.t
# Generate 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(-1, 1, 100)
for loc in locs:
basis = (lambda loc: (lambda x: np.e**(-0.5*linalg.norm(x - loc)**2)))(loc)
basis_functions.append(basis)
plt.figure()
lambs = [1e-8, 1e-6, 1e-4, 1e-2, 0]
fig_col = 3
fig_row = np.ceil(len(lambs) / fig_col)
for i, lamb in enumerate(lambs):
# Model fitting
lls = LinearLeastSquare(basis_functions=basis_functions, lamb=lamb)
lls.fit(x, t)
# Prediction
predictions = lls.predict(x_test)
std = np.sqrt(1 / lls.beta)
plt.subplot(fig_row, fig_col, i + 1)
plt.scatter(x, t, marker='x')
plt.plot(x_test[:, 0], t_test, 'r-')
plt.plot(x_test[:, 0], predictions, 'g-')
plt.plot(x_test[:, 0], predictions + std, 'g--')
plt.plot(x_test[:, 0], predictions - std, 'g--')
plt.title('$\lambda$ = {0}'.format(lamb))
plt.show()