def grad_post_mean(idx_train, w_train, idx_test, w_test, u, gp_params,
indep_noise, y, grad_u, gz):
# grad_u.shape: (#u, #gp_params)
n_gp_params = len(gp_params)
len_u = len(u)
v1 = Kinv_y(idx_train, w_train, u, len_u, indep_noise, y)
v2_1 = interp_to_u(idx_train, w_train, len_u, v1)
grad_gp_params = np.empty_like(gp_params)
for p in xrange(n_gp_params):
v2 = toeplitz_matvec(grad_u[:, p], v2_1, len_u)
v3_1 = interp_from_u(idx_train, w_train, v2)
v3_2 = Kinv_y(idx_train, w_train, u, len_u, indep_noise, v3_1)
v3_3 = interp_to_u(idx_train, w_train, len_u, v3_2)
v3 = toeplitz_matvec(u, v3_3, len_u)
g = interp_from_u(idx_test, w_test, v2 - v3)
grad_gp_params[p] = g.dot(gz)
h1 = Kinv_y(idx_train, w_train, u, len_u, indep_noise, v1)
h2 = interp_to_u(idx_train, w_train, len_u, h1)
h3 = toeplitz_matvec(u, h2, len_u)
h = -interp_from_u(idx_test, w_test, h3)
grad_noise = h.dot(gz)
return grad_gp_params, np.asarray(grad_noise)
def post_cov_y(idx_train, w_train, idx_test, w_test, u, len_u, indep_noise, y):
v1 = interp_to_u(idx_test, w_test, len_u, y[0])
v2 = toeplitz_matvec(u, v1, len_u)
v3 = interp_from_u(idx_train, w_train, v2)
v4 = Kinv_y(idx_train, w_train, u, len_u, indep_noise, v3)
v5 = interp_to_u(idx_train, w_train, len_u, v4)
v6 = toeplitz_matvec(u, v5, len_u)
f = interp_from_u(idx_test, w_test, v2 - v6)
#f = f + regularizer * y
return f[np.newaxis]
def post_mean(idx_train, w_train, idx_test, w_test, u, len_u, indep_noise, y):
#print 'condition number', cond(idx_train, w_train, u, len_u, indep_noise)
v1 = Kinv_y(idx_train, w_train, u, len_u, indep_noise, y)
v2 = interp_to_u(idx_train, w_train, len_u, v1)
v3 = toeplitz_matvec(u, v2, len_u)
f = interp_from_u(idx_test, w_test, v3)
return f
def Ky(idx, w, u, len_u, indep_noise, y):
"""
compute K(idx, w, u, sigma2) y
"""
v1 = interp_to_u(idx, w, len_u, y)
v2 = toeplitz_matvec(u, v1, len_u)
v3 = interp_from_u(idx, w, v2)
return v3 + indep_noise * y
def grad_cov_ys(idx_train, w_train, idx_test, w_test, u, gp_params,
indep_noise, ys, grad_u, gz):
"""
ys.shape: (#z, #test)
grad_u.shape: (#u, #params)
gz.shape: (#z, #test)
"""
ny = ys.shape[0]
n_params = grad_u.shape[1]
len_u = len(u)
grad_gp_params = np.zeros_like(gp_params)
grad_noise = 0
for i in xrange(ny):
v1 = interp_to_u(idx_test, w_test, len_u, ys[i])
v3 = toeplitz_matvec(u, v1, len_u)
v4_1 = interp_from_u(idx_train, w_train, v3)
v4 = Kinv_y(idx_train, w_train, u, len_u, indep_noise, v4_1)
v5_1 = interp_to_u(idx_train, w_train, len_u, v4)
for p in xrange(n_params):
grad_up = grad_u[:, p]
v2 = toeplitz_matvec(grad_up, v1, len_u)
v5 = toeplitz_matvec(grad_up, v5_1, len_u)
v6_1 = interp_from_u(idx_train, w_train, v5 - v2)
v6_2 = Kinv_y(idx_train, w_train, u, len_u, indep_noise, v6_1)
v6_3 = interp_to_u(idx_train, w_train, len_u, v6_2)
v6 = toeplitz_matvec(u, v6_3, len_u)
g = interp_from_u(idx_test, w_test, v2 - v5 + v6)
grad_gp_params[p] += g.dot(gz[i])
h1 = Kinv_y(idx_train, w_train, u, len_u, indep_noise, v4)
h2 = interp_to_u(idx_train, w_train, len_u, h1)
h3 = toeplitz_matvec(u, h2, len_u)
h = interp_from_u(idx_test, w_test, h3)
grad_noise += h.dot(gz[i])
grad_ys = post_cov_ys(idx_train, w_train, idx_test, w_test, u, len_u,
indep_noise, gz)
return grad_gp_params, np.asarray(grad_noise), grad_ys