def sufficient_statistics(self):
A, Q = self.get_dynamics()
Q_inv = T.matrix_inverse(Q)
Q_inv_A = T.matrix_solve(Q, A)
return [
-0.5 * Q_inv,
Q_inv_A,
-0.5 * T.einsum('hba,hbc->hac', A, Q_inv_A),
-0.5 * T.logdet(Q)
]
def get_stat(x, name, feed_dict={}):
node = get_current_graph().get_node(x)
print(x, name)
if node is not None:
return node.get_stat(name, feed_dict=feed_dict)
if name == 'x':
return x
elif name == 'xxT':
return T.outer(x, x)
elif name == '-0.5S^-1':
return -0.5 * T.matrix_inverse(x)
elif name == '-0.5log|S|':
return -0.5 * T.logdet(x)
raise Exception()
def log_z(self, parameter_type='regular', stop_gradient=False):
if parameter_type == 'regular':
sigma, mu = self.get_parameters('regular', stop_gradient=stop_gradient)
d = T.to_float(self.shape()[-1])
hsi, hlds = Stats.HSI(sigma), Stats.HLDS(sigma)
mmT = Stats.XXT(mu)
return (
- T.sum(hsi * mmT, [-1, -2]) - hlds
+ d / 2. * np.log(2 * np.pi)
)
else:
natparam = self.get_parameters('natural', stop_gradient=stop_gradient)
d = T.to_float(self.shape()[-1])
J, m = natparam[Stats.XXT], natparam[Stats.X]
return (
- 0.25 * (m[..., None, :]@T.matrix_inverse(J)@m[..., None])[..., 0, 0]
- 0.5 * T.logdet(-2 * J)
+ d / 2. * np.log(2 * np.pi)
)
def natural_to_regular(cls, natural_parameters):
J, m = natural_parameters[Stats.XXT], natural_parameters[Stats.X]
sigma = -0.5 * T.matrix_inverse(J)
mu = T.matmul(sigma, m[..., None])[..., 0]
return [sigma, mu]
def compute(self, A):
return -0.5 * T.matrix_inverse(A)