def test_lds_sample(T=25, D=4):
"""
Test lds_sample correctness
"""
As, bs, Qi_sqrts, ms, Ri_sqrts = make_lds_parameters(T, D)
J_diag, J_lower_diag, h = convert_lds_to_block_tridiag(As, bs, Qi_sqrts, ms, Ri_sqrts)
# Convert to dense matrix
J_full = np.zeros((T*D, T*D))
for t in range(T):
J_full[t*D:(t+1)*D, t*D:(t+1)*D] = J_diag[t]
for t in range(T-1):
J_full[t*D:(t+1)*D, (t+1)*D:(t+2)*D] = J_lower_diag[t].T
J_full[(t+1)*D:(t+2)*D, t*D:(t+1)*D] = J_lower_diag[t]
z = npr.randn(T*D,)
# Sample directly
L = np.linalg.cholesky(J_full)
xtrue = np.linalg.solve(L.T, z).reshape(T, D)
xtrue += np.linalg.solve(J_full, h.reshape(T*D)).reshape(T, D)
# Solve with the banded solver
xtest = lds_sample(As, bs, Qi_sqrts, ms, Ri_sqrts, z=z)
assert np.allclose(xtrue, xtest)
def _gibbs_sample_continuous_states(arhmm,
discrete_states,
indicators,
mog,
beta=1):
"""
Gibbs sample the continuous states given the discrete states,
the indicators, and the mixture of Gaussian model.
Beta scales the natural parameters of the MoG potential
J = Sigma^{-1}
h = Sigma^{-1} \mu = J \mu
When beta = 0, the MoG potential is ignored.
When beta = 1, the MoG potential is a normalized probability on x
To get the mean parameters, set \mu = J^{-1} h. This is unchanged by beta.
"""
# Extract the dynamics parameters
As = arhmm.observations.As[discrete_states[1:]]
bs = arhmm.observations.bs[discrete_states[1:]]
Qi_sqrts = np.linalg.cholesky(np.linalg.inv(arhmm.observations.Sigmas))
Qi_sqrts = Qi_sqrts[discrete_states[1:]]
# Extract the observation potentials
ms = mog.observations.mus[indicators]
Ri_sqrts = np.linalg.cholesky(np.linalg.inv(mog.observations.Sigmas))
Ri_sqrts = Ri_sqrts[indicators]
# Call the forward filter backward sample code
return lds_sample(As, bs, Qi_sqrts, ms,
1e-4 * np.eye(arhmm.D) + np.sqrt(beta) * Ri_sqrts)
def sample(self):
return [lds_sample(*prms) for prms in self.params]
