def check_extra_loglike_terms(A, B, C, D, mu_init, sigma_init, data):
ex1 = LDSStates._extra_loglike_terms(
A, B.dot(B.T), C, D.dot(D.T), mu_init, sigma_init, data)
ex2 = LDSStates._info_extra_loglike_terms(
*extra_info_params(A, B, C, D, mu_init, sigma_init, data))
assert np.isclose(ex1, ex2)
def check_extra_loglike_terms(A, B, C, D, mu_init, sigma_init, data):
ex1 = LDSStates._extra_loglike_terms(A, B.dot(B.T), C, D.dot(D.T), mu_init,
sigma_init, data)
ex2 = LDSStates._info_extra_loglike_terms(
*extra_info_params(A, B, C, D, mu_init, sigma_init, data))
assert np.isclose(ex1, ex2)
def check_filters(A, B, C, D, mu_init, sigma_init, data):
def info_normalizer(J, h):
out = 0.
out += 1 / 2. * h.dot(np.linalg.solve(J, h))
out -= 1 / 2. * np.linalg.slogdet(J)[1]
out += h.shape[0] / 2. * np.log(2 * np.pi)
return out
ll, filtered_mus, filtered_sigmas = kalman_filter(mu_init, sigma_init, A,
B.dot(B.T), C,
D.dot(D.T), data)
py_partial_ll = info_normalizer(
*dense_infoparams(A, B, C, D, mu_init, sigma_init, data))
partial_ll, filtered_Js, filtered_hs = kalman_info_filter(
*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)
filtered_mus2 = [
np.linalg.solve(J, h) for J, h in zip(filtered_Js, filtered_hs)
]
filtered_sigmas2 = [np.linalg.inv(J) for J in filtered_Js]
assert all(
np.allclose(mu1, mu2) for mu1, mu2 in zip(filtered_mus, filtered_mus2))
assert all(
np.allclose(s1, s2)
for s1, s2 in zip(filtered_sigmas, filtered_sigmas2))
assert np.isclose(partial_ll, py_partial_ll)
assert np.isclose(ll, ll2)
def check_filters(A, B, C, D, mu_init, sigma_init, data):
def info_normalizer(J,h):
out = 0.
out += 1/2. * h.dot(np.linalg.solve(J,h))
out -= 1/2. * np.linalg.slogdet(J)[1]
out += h.shape[0]/2. * np.log(2*np.pi)
return out
ll, filtered_mus, filtered_sigmas = kalman_filter(
mu_init, sigma_init, A, B.dot(B.T), C, D.dot(D.T), data)
py_partial_ll = info_normalizer(*dense_infoparams(
A, B, C, D, mu_init, sigma_init, data))
partial_ll, filtered_Js, filtered_hs = kalman_info_filter(
*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)
filtered_mus2 = [np.linalg.solve(J,h) for J, h in zip(filtered_Js, filtered_hs)]
filtered_sigmas2 = [np.linalg.inv(J) for J in filtered_Js]
assert all(np.allclose(mu1, mu2)
for mu1, mu2 in zip(filtered_mus, filtered_mus2))
assert all(np.allclose(s1, s2)
for s1, s2 in zip(filtered_sigmas, filtered_sigmas2))
assert np.isclose(partial_ll, py_partial_ll)
assert np.isclose(ll, ll2)
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 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)
