def _construct_proposal_covariance(self, y):
"""
Helper method to compute Cholesky factor of the Gaussian Kameleon-lite proposal centred at y.
"""
# compute gradient projection
grad_phi_y = feature_map_grad_single(y, self.omega, self.u)
# construct covariance, adding exploration noise
R = self.gamma2 * np.eye(self.D) + self.step_size * np.dot(grad_phi_y, (self.m ** 2) * np.dot(self.C, grad_phi_y.T))
L_R = np.linalg.cholesky(R)
return L_R
def _construct_proposal_covariance(self, y):
"""
Helper method to compute Cholesky factor of the Gaussian Kameleon-lite proposal centred at y.
"""
# compute gradient projection
grad_phi_y = feature_map_grad_single(y, self.omega, self.u)
# construct covariance, adding exploration noise
R = self.gamma2 * np.eye(self.D) + self.step_size * np.dot(
grad_phi_y, (self.m**2) * np.dot(self.C, grad_phi_y.T))
L_R = np.linalg.cholesky(R)
return L_R
eta = 50.
plt.plot(Z[:, 0], Z[:, 1], 'bx')
# proposal plotting colors
colors = ['y', 'r', 'g', 'm', 'black']
# proposals centred at those points
Ys = np.array([[-20, 9.7], [-10, 0], [0,-3], [10, 0], [20, 9.7]])
for j in range(len(colors)):
# pick point at random, embed, gradient
y = Ys[j]
phi_y = feature_map_single(y, omega, u)
grad_phi_y = feature_map_grad_single(y, omega, u)
# draw a number of proposals at the current point
n_proposals = 100
X_star = np.zeros((n_proposals, D))
# generate proposal samples in feature space
for i in range(n_proposals):
plt.plot(y[0], y[1], '*', markersize=15, color=colors[j])
# construct covariance, adding exploration noise
R = eta**2 * np.dot(grad_phi_y, np.dot(C, grad_phi_y.T))
L_R = np.linalg.cholesky(R)
# sample proposal
x_star = sample_gaussian(N=1, mu=y, Sigma=L_R, is_cholesky=True)
