def _build_marginal_likelihood_logp(self, y, X, Xu, sigma):
sigma2 = tt.square(sigma)
Kuu = self.cov_func(Xu)
Kuf = self.cov_func(Xu, X)
Luu = cholesky(stabilize(Kuu))
A = solve_lower(Luu, Kuf)
Qffd = tt.sum(A * A, 0)
if self.approx == "FITC":
Kffd = self.cov_func(X, diag=True)
Lamd = tt.clip(Kffd - Qffd, 0.0, np.inf) + sigma2
trace = 0.0
elif self.approx == "VFE":
Lamd = tt.ones_like(Qffd) * sigma2
trace = ((1.0 / (2.0 * sigma2)) *
(tt.sum(self.cov_func(X, diag=True)) -
tt.sum(tt.sum(A * A, 0))))
else: # DTC
Lamd = tt.ones_like(Qffd) * sigma2
trace = 0.0
A_l = A / Lamd
L_B = cholesky(tt.eye(Xu.shape[0]) + tt.dot(A_l, tt.transpose(A)))
r = y - self.mean_func(X)
r_l = r / Lamd
c = solve_lower(L_B, tt.dot(A, r_l))
constant = 0.5 * X.shape[0] * tt.log(2.0 * np.pi)
logdet = 0.5 * tt.sum(tt.log(Lamd)) + tt.sum(tt.log(tt.diag(L_B)))
quadratic = 0.5 * (tt.dot(r, r_l) - tt.dot(c, c))
return -1.0 * (constant + logdet + quadratic + trace)
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)
def _build_marginal_likelihood_logp(self, y, X, Xu, sigma):
sigma2 = tt.square(sigma)
Kuu = self.cov_func(Xu)
Kuf = self.cov_func(Xu, X)
Luu = cholesky(stabilize(Kuu))
A = solve_lower(Luu, Kuf)
Qffd = tt.sum(A * A, 0)
if self.approx == "FITC":
Kffd = self.cov_func(X, diag=True)
Lamd = tt.clip(Kffd - Qffd, 0.0, np.inf) + sigma2
trace = 0.0
elif self.approx == "VFE":
Lamd = tt.ones_like(Qffd) * sigma2
trace = ((1.0 / (2.0 * sigma2)) *
(tt.sum(self.cov_func(X, diag=True)) -
tt.sum(tt.sum(A * A, 0))))
else: # DTC
Lamd = tt.ones_like(Qffd) * sigma2
trace = 0.0
A_l = A / Lamd
L_B = cholesky(tt.eye(Xu.shape[0]) + tt.dot(A_l, tt.transpose(A)))
r = y - self.mean_func(X)
r_l = r / Lamd
c = solve_lower(L_B, tt.dot(A, r_l))
constant = 0.5 * X.shape[0] * tt.log(2.0 * np.pi)
logdet = 0.5 * tt.sum(tt.log(Lamd)) + tt.sum(tt.log(tt.diag(L_B)))
quadratic = 0.5 * (tt.dot(r, r_l) - tt.dot(c, c))
return -1.0 * (constant + logdet + quadratic + trace)
def _build_conditional(self, Xnew, X, f, cov_total, mean_total):
Kxx = cov_total(X)
Kxs = self.cov_func(X, Xnew)
L = cholesky(stabilize(Kxx))
A = solve_lower(L, Kxs)
v = solve_lower(L, f - mean_total(X))
mu = self.mean_func(Xnew) + tt.dot(tt.transpose(A), v)
Kss = self.cov_func(Xnew)
cov = Kss - tt.dot(tt.transpose(A), A)
return mu, cov
def _build_conditional(self, Xnew, X, f, cov_total, mean_total):
Kxx = cov_total(X)
Kxs = self.cov_func(X, Xnew)
L = cholesky(stabilize(Kxx))
A = solve_lower(L, Kxs)
v = solve_lower(L, f - mean_total(X))
mu = self.mean_func(Xnew) + tt.dot(tt.transpose(A), v)
Kss = self.cov_func(Xnew)
cov = Kss - tt.dot(tt.transpose(A), A)
return mu, cov
def get_mean_var1(choices, actions, rewards, kern):
Kxx = kern(actions)
Kxs = kern(actions, choices)
L = cholesky(stabilize(Kxx))
A = solve_lower(L, Kxs)
v = solve_lower(L, rewards)
mu = tt.dot(tt.transpose(A), v)
Kss = kern(choices, diag=True)
var = Kss - tt.sum(tt.square(A), 0)
return mu, var
def _build_conditional(self, Xnew, X, f):
Kxx = self.cov_func(X)
Kxs = self.cov_func(X, Xnew)
Kss = self.cov_func(Xnew)
L = cholesky(stabilize(Kxx))
A = solve_lower(L, Kxs)
cov = Kss - tt.dot(tt.transpose(A), A)
v = solve_lower(L, f - self.mean_func(X))
mu = self.mean_func(Xnew) + tt.dot(tt.transpose(A), v)
beta = tt.dot(v, v)
nu2 = self.nu + X.shape[0]
covT = (self.nu + beta - 2)/(nu2 - 2) * cov
return nu2, mu, covT
def _build_conditional(self, Xnew, X, f):
Kxx = self.cov_func(X)
Kxs = self.cov_func(X, Xnew)
Kss = self.cov_func(Xnew)
L = cholesky(stabilize(Kxx))
A = solve_lower(L, Kxs)
cov = Kss - tt.dot(tt.transpose(A), A)
v = solve_lower(L, f - self.mean_func(X))
mu = self.mean_func(Xnew) + tt.dot(tt.transpose(A), v)
beta = tt.dot(v, v)
nu2 = self.nu + X.shape[0]
covT = (self.nu + beta - 2) / (nu2 - 2) * cov
return nu2, mu, covT
def _build_conditional(self, Xnew, pred_noise, diag, X, y, noise, cov_total, mean_total):
Kxx = cov_total(X)
Kxs = self.cov_func(X, Xnew)
Knx = noise(X)
rxx = y - mean_total(X)
L = cholesky(stabilize(Kxx) + Knx)
A = solve_lower(L, Kxs)
v = solve_lower(L, rxx)
mu = self.mean_func(Xnew) + tt.dot(tt.transpose(A), v)
if diag:
Kss = self.cov_func(Xnew, diag=True)
var = Kss - tt.sum(tt.square(A), 0)
if pred_noise:
var += noise(Xnew, diag=True)
return mu, var
else:
Kss = self.cov_func(Xnew)
cov = Kss - tt.dot(tt.transpose(A), A)
if pred_noise:
cov += noise(Xnew)
return mu, cov if pred_noise else stabilize(cov)
def _build_conditional(self, Xnew, pred_noise, diag, X, y, noise,
cov_total, mean_total):
Kxx = cov_total(X)
Kxs = self.cov_func(X, Xnew)
Knx = noise(X)
rxx = y - mean_total(X)
L = cholesky(stabilize(Kxx) + Knx)
A = solve_lower(L, Kxs)
v = solve_lower(L, rxx)
mu = self.mean_func(Xnew) + tt.dot(tt.transpose(A), v)
if diag:
Kss = self.cov_func(Xnew, diag=True)
var = Kss - tt.sum(tt.square(A), 0)
if pred_noise:
var += noise(Xnew, diag=True)
return mu, var
else:
Kss = self.cov_func(Xnew)
cov = Kss - tt.dot(tt.transpose(A), A)
if pred_noise:
cov += noise(Xnew)
return mu, stabilize(cov)
