def second_moments(i, j, M2, beta, R, logk_c, logk_r, z_, Sx, *args):
# This comes from Deisenroth's thesis ( Eqs 2.51- 2.54 )
Rij = R[i, j]
n2 = logk_c[i] + logk_r[j]
n2 += utils.maha(z_[i], -z_[j], 0.5 * solve(Rij, Sx))
Q = tt.exp(n2) / tt.sqrt(det(Rij))
# Eq 2.55
m2 = matrix_dot(beta[i], Q, beta[j])
m2 = theano.ifelse.ifelse(tt.eq(i, j), m2 + 1e-6, m2)
M2 = tt.set_subtensor(M2[i, j], m2)
return M2
def SEard(hyp, X1, X2=None, all_pairs=True):
''' Squard exponential kernel with diagonal scaling matrix
(one lengthscale per dimension)'''
n = 1
idims = 1
if X1.ndim == 2:
n, idims = X1.shape
elif X2.ndim == 2:
n, idims = X2.shape
else:
idims = X1.shape[0]
sf2 = hyp[idims]**2
if (not all_pairs) and (X1 is X2 or X2 is None):
# all the distances are going to be zero
K = tt.tile(sf2, (n,))
return K
ls2 = hyp[:idims]**2
D = utils.maha(X1, X2, tt.diag(1.0/ls2),
all_pairs=all_pairs)
K = sf2*tt.exp(-0.5*D)
return K