def info_E_step(self):
self._normalizer, self.smoothed_mus, \
self.smoothed_sigmas, E_xtp1_xtT = \
info_E_step(*self.info_params)
self._set_expected_stats(self.smoothed_mus, self.smoothed_sigmas,
E_xtp1_xtT)
def E_step(self, verbose=False):
self.gaussian_states = self.laplace_approximation(verbose=verbose)
# Compute normalizer and covariances with E step
T, D = self.T, self.D_latent
H_diag, H_upper_diag = self.sparse_hessian_log_joint(
self.gaussian_states)
J_init = J_11 = J_22 = np.zeros((D, D))
h_init = h_1 = h_2 = np.zeros((D, ))
# Negate the Hessian since precision is -H
J_21 = np.swapaxes(-H_upper_diag, -1, -2)
J_node = -H_diag
h_node = np.zeros((T, D))
logZ, _, self.smoothed_sigmas, E_xtp1_xtT = \
info_E_step(J_init, h_init, 0,
J_11, J_21, J_22, h_1, h_2, np.zeros((T - 1)),
J_node, h_node, np.zeros(T))
# Laplace approximation -- normalizer is the joint times
# the normalizer from the Gaussian approx.
self._normalizer = self.log_joint(self.gaussian_states) + logZ
self._set_expected_stats(self.gaussian_states, self.smoothed_sigmas,
E_xtp1_xtT)
def check_info_Estep(A, B, sigma_states, C, D, sigma_obs, mu_init, sigma_init,
inputs, data):
ll, smoothed_mus, smoothed_sigmas, ExnxT = E_step(mu_init, sigma_init, A,
B, sigma_states, C, D,
sigma_obs, inputs, data)
ll2, smoothed_mus2, smoothed_sigmas2, ExnxT2 = info_E_step(
*info_params(A, B, sigma_states, C, D, sigma_obs, mu_init, sigma_init,
data, inputs))
assert np.isclose(ll, ll2)
assert np.allclose(smoothed_mus, smoothed_mus2)
assert np.allclose(smoothed_sigmas, smoothed_sigmas2)
assert np.allclose(ExnxT, ExnxT2)
def check_info_Estep(A, B, C, D, mu_init, sigma_init, data):
ll, smoothed_mus, smoothed_sigmas, ExnxT = E_step(
mu_init, sigma_init, A, B.dot(B.T), C, D.dot(D.T), data)
partial_ll, smoothed_mus2, smoothed_sigmas2, ExnxT2 = info_E_step(
*info_params(A, B, C, D, mu_init, sigma_init, data))
ll2 = partial_ll + LDSStates._extra_loglike_terms(
A, B.dot(B.T), C, D.dot(D.T), mu_init, sigma_init, data)
assert np.isclose(ll,ll2)
assert np.allclose(smoothed_mus, smoothed_mus2)
assert np.allclose(smoothed_sigmas, smoothed_sigmas2)
assert np.allclose(ExnxT, ExnxT2)
def check_info_Estep(A, B, C, D, mu_init, sigma_init, data):
ll, smoothed_mus, smoothed_sigmas, ExnxT = E_step(mu_init, sigma_init, A,
B.dot(B.T), C,
D.dot(D.T), data)
partial_ll, smoothed_mus2, smoothed_sigmas2, ExnxT2 = info_E_step(
*info_params(A, B, C, D, mu_init, sigma_init, data))
ll2 = partial_ll + LDSStates._extra_loglike_terms(A, B.dot(
B.T), C, D.dot(D.T), mu_init, sigma_init, data)
assert np.isclose(ll, ll2)
assert np.allclose(smoothed_mus, smoothed_mus2)
assert np.allclose(smoothed_sigmas, smoothed_sigmas2)
assert np.allclose(ExnxT, ExnxT2)
def solve_symm_block_tridiag(H_diag, H_upper_diag, v):
"""
use the info smoother to solve a symmetric block tridiagonal system
"""
T, D, _ = H_diag.shape
assert H_diag.ndim == 3 and H_diag.shape[2] == D
assert H_upper_diag.shape == (T - 1, D, D)
assert v.shape == (T, D)
J_init = J_11 = J_22 = np.zeros((D, D))
h_init = h_1 = h_2 = np.zeros((D, ))
J_21 = np.swapaxes(H_upper_diag, -1, -2)
J_node = H_diag
h_node = v
_, y, _, _ = info_E_step(J_init, h_init, 0, J_11, J_21, J_22, h_1, h_2,
np.zeros((T - 1)), J_node, h_node, np.zeros(T))
return y
def compute_symm_block_tridiag_covariances(H_diag, H_upper_diag):
"""
use the info smoother to solve a symmetric block tridiagonal system
"""
T, D, _ = H_diag.shape
assert H_diag.ndim == 3 and H_diag.shape[2] == D
assert H_upper_diag.shape == (T - 1, D, D)
J_init = J_11 = J_22 = np.zeros((D, D))
h_init = h_1 = h_2 = np.zeros((D, ))
J_21 = np.swapaxes(H_upper_diag, -1, -2)
J_node = H_diag
h_node = np.zeros((T, D))
_, _, sigmas, E_xt_xtp1 = \
info_E_step(J_init, h_init, 0,
J_11, J_21, J_22, h_1, h_2, np.zeros((T-1)),
J_node, h_node, np.zeros(T))
return sigmas, E_xt_xtp1
def check_info_Estep(A, B, C, D, mu_init, sigma_init, data):
def Covxxn_to_ExnxT(Covxxn, smoothed_mus):
outs = np.empty_like(Covxxn)
for out, cov, mu_t, mu_tp1 in zip(outs,Covxxn, smoothed_mus[:-1], smoothed_mus[1:]):
out[...] = cov.T + np.outer(mu_tp1,mu_t)
return outs
ll, smoothed_mus, smoothed_sigmas, ExnxT = E_step(
mu_init, sigma_init, A, B.dot(B.T), C, D.dot(D.T), data)
partial_ll, smoothed_mus2, smoothed_sigmas2, Covxxn = info_E_step(
*info_params(A, B, C, D, mu_init, sigma_init, data))
ll2 = partial_ll + extra_loglike_terms(
A, B, C, D, mu_init, sigma_init, data)
ExnxT2 = Covxxn_to_ExnxT(Covxxn,smoothed_mus2)
assert np.isclose(ll,ll2)
assert np.allclose(smoothed_mus, smoothed_mus2)
assert np.allclose(smoothed_sigmas, smoothed_sigmas2)
assert np.allclose(ExnxT, ExnxT2)
def check_info_Estep(A, B, C, D, mu_init, sigma_init, data):
def Covxxn_to_ExnxT(Covxxn, smoothed_mus):
outs = np.empty_like(Covxxn)
for out, cov, mu_t, mu_tp1 in zip(outs, Covxxn, smoothed_mus[:-1],
smoothed_mus[1:]):
out[...] = cov.T + np.outer(mu_tp1, mu_t)
return outs
ll, smoothed_mus, smoothed_sigmas, ExnxT = E_step(mu_init, sigma_init, A,
B.dot(B.T), C,
D.dot(D.T), data)
partial_ll, smoothed_mus2, smoothed_sigmas2, Covxxn = info_E_step(
*info_params(A, B, C, D, mu_init, sigma_init, data))
ll2 = partial_ll + extra_loglike_terms(A, B, C, D, mu_init, sigma_init,
data)
ExnxT2 = Covxxn_to_ExnxT(Covxxn, smoothed_mus2)
assert np.isclose(ll, ll2)
assert np.allclose(smoothed_mus, smoothed_mus2)
assert np.allclose(smoothed_sigmas, smoothed_sigmas2)
assert np.allclose(ExnxT, ExnxT2)
def meanfield_update_gaussian_states(self):
J_init = np.linalg.inv(self.sigma_init)
h_init = np.linalg.solve(self.sigma_init, self.mu_init)
def get_paramseq(distns):
contract = partial(np.tensordot, self.expected_states, axes=1)
std_param = lambda d: d._natural_to_standard(d.mf_natural_hypparam)
params = [mniw_expectedstats(*std_param(d)) for d in distns]
return map(contract, zip(*params))
J_pair_22, J_pair_21, J_pair_11, logdet_pair = \
get_paramseq(self.dynamics_distns)
J_yy, J_yx, J_node, logdet_node = get_paramseq(self.emission_distns)
h_node = np.einsum('ni,nij->nj', self.data, J_yx)
self._mf_lds_normalizer, self.smoothed_mus, self.smoothed_sigmas, \
E_xtp1_xtT = info_E_step(
J_init,h_init,J_pair_11,-J_pair_21,J_pair_22,J_node,h_node)
self._mf_lds_normalizer += LDSStates._info_extra_loglike_terms(
J_init, h_init, logdet_pair, J_yy, logdet_node, self.data)
self._set_gaussian_expected_stats(
self.smoothed_mus,self.smoothed_sigmas,E_xtp1_xtT)
def meanfieldupdate(self):
self._mf_lds_normalizer, self.smoothed_mus, self.smoothed_sigmas, \
E_xtp1_xtT = info_E_step(*self.expected_info_params)
self._set_expected_stats(self.smoothed_mus, self.smoothed_sigmas,
E_xtp1_xtT)
