def __init__(self):
self.real_dim = 2
self.active_dim = 1
self.no_samples = 100
self.kernel = TripathyMaternKernel(self.real_dim, self.active_dim)
# Parameters
self.sn = 0.1 # 1e-7 # 0.1
self.W = self.kernel.sample_W()
self.function = AugmentedSinusoidal()
self.real_W = np.asarray([
[3],
[1]
])
self.real_W = self.real_W / np.linalg.norm(self.real_W)
# [[0.9486833]
# [0.31622777]]
x_range = np.linspace(0., 1., int(np.sqrt(self.no_samples)))
y_range = np.linspace(0., 1., int(np.sqrt(self.no_samples)))
self.X = cartesian([x_range, y_range])
#self.X = np.random.rand(self.no_samples, self.real_dim)
print(self.X.shape)
Z = np.dot(self.X, self.real_W).reshape(-1, 1)
print(Z.shape)
self.Y = self.function.f(Z.T).reshape(-1, 1)
self.optimizer = TripathyOptimizer()
self.no_tries = 1
self.PLOT_MEAN = True
def visualize_quadratic_function(self):
x_range = np.linspace(0., 1., 80)
y_range = np.linspace(0., 1., 80)
X = cartesian([x_range, y_range])
import os
if not os.path.exists("./pics/"):
os.makedirs("./pics/")
#################################
# TRAIN THE W_OPTIMIZER #
#################################
Opt = TripathyOptimizer()
for j in range(self.no_tries):
print("Try number : ", j)
W_hat = self.kernel.sample_W()
self.kernel.update_params(
W=W_hat,
s=self.kernel.inner_kernel.variance,
l=self.kernel.inner_kernel.lengthscale
)
W_hat, sn, l, s = Opt.run_two_step_optimization(self.kernel, self.sn, self.X, self.Y)
# Create the gp_regression function and pass in the predictor function as f_hat
self.kernel.update_params(W=W_hat, l=l, s=s)
gp_reg = GPRegression(self.X, self.Y, self.kernel, noise_var=sn)
y = self.function.f( np.dot(X, self.real_W).T )
y_hat = gp_reg.predict(self.X)[0].squeeze()
#################################
# END TRAIN THE W_OPTIMIZER #
#################################
fig = plt.figure()
ax = Axes3D(fig)
# First plot the real function
ax.scatter(X[:,0], X[:, 1], y, s=1)
ax.scatter(self.X[:,0], self.X[:, 1], y_hat, cmap=plt.cm.jet)
fig.savefig('./pics/Iter_' + str(j) + '.png', )
# plt.show()
plt.close(fig)
# Save the W just in case
l = loss(
self.kernel,
W_hat,
sn,
s,
l,
self.X,
self.Y
)
np.savetxt("./pics/Iter_" + str(j) + "__" + "Loss_" + str(l) + ".txt", W_hat)
def plot_3d(self, y_hat, title):
# Plot real function
x1 = np.linspace(-1, 1, 100)
x2 = np.linspace(-1, 1, 100)
x_real = cartesian([x1, x2])
y_real = self.f_env(x_real, disp=True)
# Create the plot
fig = plt.figure()
ax = Axes3D(fig)
ax.view_init(azim=30)
# First plot the real function
ax.scatter(x_real[:, 0], x_real[:, 1], y_real, 'k.', alpha=.3, s=1)
ax.scatter(self.X[:, 0], self.X[:, 1], y_hat, cmap=plt.cm.jet)
fig.savefig('./featureSelection/' + title + '.png')
plt.show()
def visualize_augmented_sinusoidal_function(self):
x_range = np.linspace(0., 1., 80)
y_range = np.linspace(0., 1., 80)
X = cartesian([x_range, y_range])
import os
if not os.path.exists("./pics-twostep/"):
os.makedirs("./pics-twostep/")
#################################
# TRAIN THE W_OPTIMIZER #
#################################
Opt = TripathyOptimizer()
print("Real hidden matrix is: ", self.real_W)
W_hat = self.kernel.sample_W()
self.kernel.update_params(
W=W_hat,
s=self.kernel.inner_kernel.variance,
l=self.kernel.inner_kernel.lengthscale
)
W_hat, sn, l, s = Opt.try_two_step_optimization_with_restarts(self.kernel, self.X, self.Y)
# TODO: Check if these values are attained over multiple iterations (check if assert otherwise fails)
# Create the gp_regression function and pass in the predictor function as f_hat
self.kernel.update_params(W=W_hat, l=l, s=s)
gp_reg = GPRegression(self.X, self.Y, self.kernel, noise_var=sn)
y = self.function.f( np.dot(X, self.real_W).T )
if self.PLOT_MEAN:
y_hat = gp_reg.predict(X)[0].squeeze()
else:
y_hat = gp_reg.predict(self.X)[0].squeeze()
#################################
# END TRAIN THE W_OPTIMIZER #
#################################
fig = plt.figure()
ax = Axes3D(fig)
# First plot the real function
ax.scatter(X[:,0], X[:, 1], y, s=1)
if self.PLOT_MEAN:
ax.scatter(X[:, 0], X[:, 1], y_hat, cmap=plt.cm.jet)
else:
ax.scatter(self.X[:,0], self.X[:, 1], y_hat, cmap=plt.cm.jet)
# Save the W just in case
l = loss(
self.kernel,
W_hat,
sn,
s,
l,
self.X,
self.Y
)
fig.savefig('./pics-twostep/BestLoss_' + str(l) + '.png', )
plt.show()
plt.close(fig)
np.savetxt("./pics-twostep/BestLoss_" + str(l) + ".txt", W_hat)