def _build_prior(self, name, Xs, jitter, **kwargs):
self.N = int(np.prod([len(X) for X in Xs]))
mu = self.mean_func(cartesian(*Xs))
chols = [cholesky(stabilize(cov(X), jitter)) for cov, X in zip(self.cov_funcs, Xs)]
v = pm.Normal(name + "_rotated_", mu=0.0, sigma=1.0, size=self.N, **kwargs)
f = pm.Deterministic(name, mu + at.flatten(kron_dot(chols, v)))
return f
def test_kron_dot():
np.random.seed(1)
# Create random matrices
Ks = [np.random.rand(3, 3) for i in range(3)]
# Create random vector with correct shape
tot_size = np.prod([k.shape[1] for k in Ks])
x = np.random.rand(tot_size).reshape((tot_size, 1))
# Construct entire kronecker product then multiply
big = kronecker(*Ks)
slow_ans = at.dot(big, x)
# Use tricks to avoid construction of entire kronecker product
fast_ans = kron_dot(Ks, x)
np.testing.assert_array_almost_equal(slow_ans.eval(), fast_ans.eval())
def _build_conditional(self, Xnew, pred_noise, diag):
Xs, y, sigma = self.Xs, self.y, self.sigma
# Old points
X = cartesian(*Xs)
delta = y - self.mean_func(X)
Kns = [f(x) for f, x in zip(self.cov_funcs, Xs)]
eigs_sep, Qs = zip(*map(eigh, Kns)) # Unzip
QTs = list(map(at.transpose, Qs))
eigs = kron_diag(*eigs_sep) # Combine separate eigs
if sigma is not None:
eigs += sigma ** 2
# New points
Km = self.cov_func(Xnew, diag=diag)
Knm = self.cov_func(X, Xnew)
Kmn = Knm.T
# Build conditional mu
alpha = kron_dot(QTs, delta)
alpha = alpha / eigs[:, None]
alpha = kron_dot(Qs, alpha)
mu = at.dot(Kmn, alpha).ravel() + self.mean_func(Xnew)
# Build conditional cov
A = kron_dot(QTs, Knm)
A = A / at.sqrt(eigs[:, None])
if diag:
Asq = at.sum(at.square(A), 0)
cov = Km - Asq
if pred_noise:
cov += sigma
else:
Asq = at.dot(A.T, A)
cov = Km - Asq
if pred_noise:
cov += sigma * at.identity_like(cov)
return mu, cov