def actual_normal_log_normalizer(natparam, factors, sizes):
def make_dense_precision_matrix(natparam, sizes):
dims = [sum(sizes[:n]) for n in range(len(sizes) + 1)]
prec = np.zeros((dims[-1], dims[-1]))
for factor, minusJ in natparam.xi_xjtrs.iteritems():
node1, node2 = factor
prec[dims[node1]:dims[node1 + 1],
dims[node2]:dims[node2 + 1]] += -minusJ
prec[dims[node2]:dims[node2 + 1],
dims[node1]:dims[node1 + 1]] += -minusJ.T
for factor, minustau in natparam.xi_times_xjs.iteritems():
node1, node2 = factor
prec[dims[node1]:dims[node1+1], dims[node2]:dims[node2+1]] += \
-pgm.diag(minustau)
prec[dims[node2]:dims[node2+1], dims[node1]:dims[node1+1]] += \
-pgm.diag(minustau).T
for factor, halfminusJ in natparam.xi_xitrs.iteritems():
node, = factor
prec[dims[node]:dims[node + 1],
dims[node]:dims[node + 1]] += -2 * halfminusJ
for factor, halfminustau in natparam.xi_squareds.iteritems():
node, = factor
prec[dims[node]:dims[node+1], dims[node]:dims[node+1]] += \
-2*pgm.diag(halfminustau)
return prec
prec = make_dense_precision_matrix(natparam, sizes)
inv_prec = np.linalg.inv(prec)
h = np.concatenate([
natparam.xis.get((n, ), (np.zeros(sizes[n]), ))
for n in range(len(sizes))
])
log_normalizer = 0.5 * np.dot(h, np.dot(inv_prec, h))
log_normalizer -= 0.5 * logdet(prec) + 0.5 * sum(sizes) * np.log(2 * np.pi)
return log_normalizer
def fun(x, a, b):
return tracers.logdet(
tracers.add_n(np.einsum(',ab->ab', x, a),
np.einsum(',ab->ab', x, b)))
def log_joint(z, x):
log_prior = -1./2 * np.dot(z, z)
centered = x - np.dot(A, z)
log_like = -1./2 * np.dot(centered, np.dot(np.linalg.inv(Sigma), centered)) \
- 1./2 * logdet(Sigma)
return log_prior + log_like