def _build_conditional(self, Xnew, pred_noise, diag, X, Xu, y, sigma, cov_total, mean_total):
sigma2 = tt.square(sigma)
Kuu = cov_total(Xu)
Kuf = cov_total(Xu, X)
Luu = cholesky(stabilize(Kuu))
A = solve_lower(Luu, Kuf)
Qffd = tt.sum(A * A, 0)
if self.approx == "FITC":
Kffd = cov_total(X, diag=True)
Lamd = tt.clip(Kffd - Qffd, 0.0, np.inf) + sigma2
else: # VFE or DTC
Lamd = tt.ones_like(Qffd) * sigma2
A_l = A / Lamd
L_B = cholesky(tt.eye(Xu.shape[0]) + tt.dot(A_l, tt.transpose(A)))
r = y - mean_total(X)
r_l = r / Lamd
c = solve_lower(L_B, tt.dot(A, r_l))
Kus = self.cov_func(Xu, Xnew)
As = solve_lower(Luu, Kus)
mu = self.mean_func(Xnew) + tt.dot(tt.transpose(As), solve_upper(tt.transpose(L_B), c))
C = solve_lower(L_B, As)
if diag:
Kss = self.cov_func(Xnew, diag=True)
var = Kss - tt.sum(tt.square(As), 0) + tt.sum(tt.square(C), 0)
if pred_noise:
var += sigma2
return mu, var
else:
cov = (self.cov_func(Xnew) - tt.dot(tt.transpose(As), As) +
tt.dot(tt.transpose(C), C))
if pred_noise:
cov += sigma2 * tt.identity_like(cov)
return mu, stabilize(cov)
def _build_conditional(self, Xnew, pred_noise, diag, X, Xu, y, sigma,
cov_total, mean_total):
sigma2 = tt.square(sigma)
Kuu = cov_total(Xu)
Kuf = cov_total(Xu, X)
Luu = cholesky(stabilize(Kuu))
A = solve_lower(Luu, Kuf)
Qffd = tt.sum(A * A, 0)
if self.approx == "FITC":
Kffd = cov_total(X, diag=True)
Lamd = tt.clip(Kffd - Qffd, 0.0, np.inf) + sigma2
else: # VFE or DTC
Lamd = tt.ones_like(Qffd) * sigma2
A_l = A / Lamd
L_B = cholesky(tt.eye(Xu.shape[0]) + tt.dot(A_l, tt.transpose(A)))
r = y - mean_total(X)
r_l = r / Lamd
c = solve_lower(L_B, tt.dot(A, r_l))
Kus = self.cov_func(Xu, Xnew)
As = solve_lower(Luu, Kus)
mu = self.mean_func(Xnew) + tt.dot(tt.transpose(As),
solve_upper(tt.transpose(L_B), c))
C = solve_lower(L_B, As)
if diag:
Kss = self.cov_func(Xnew, diag=True)
var = Kss - tt.sum(tt.square(As), 0) + tt.sum(tt.square(C), 0)
if pred_noise:
var += sigma2
return mu, var
else:
cov = (self.cov_func(Xnew) - tt.dot(tt.transpose(As), As) +
tt.dot(tt.transpose(C), C))
if pred_noise:
cov += sigma2 * tt.identity_like(cov)
return mu, cov if pred_noise else stabilize(cov)
