def log_density(self, sample):
assert isinstance(sample, list) and len(sample) == len(self.datas)
logq = 0
for s, prms in zip(sample, self.params):
logq += lds_log_probability(s, *prms)
return logq
def test_lds_log_probability(T=25, D=4):
"""
Test lds_log_probability 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]
Sigma = np.linalg.inv(J_full)
mu = Sigma.dot(h.ravel()).reshape((T, D))
x = npr.randn(T, D)
from scipy.stats import multivariate_normal
ll_true = multivariate_normal.logpdf(x.ravel(), mu.ravel(), Sigma)
# Solve with the banded solver
ll_test = lds_log_probability(x, As, bs, Qi_sqrts, ms, Ri_sqrts)
assert np.allclose(ll_true, ll_test), "True LL {} != Test LL {}".format(ll_true, ll_test)
def test_lds_log_probability_perf(T=1000, D=10, N_iter=10):
"""
Compare performance of banded method vs message passing in pylds.
"""
print("Comparing methods for T={} D={}".format(T, D))
from pylds.lds_messages_interface import kalman_info_filter, kalman_filter
# Convert LDS parameters into info form for pylds
As, bs, Qi_sqrts, ms, Ri_sqrts = make_lds_parameters(T, D)
Qis = np.matmul(Qi_sqrts, np.swapaxes(Qi_sqrts, -1, -2))
Ris = np.matmul(Ri_sqrts, np.swapaxes(Ri_sqrts, -1, -2))
x = npr.randn(T, D)
print("Timing banded method")
start = time.time()
for itr in range(N_iter):
lds_log_probability(x, As, bs, Qi_sqrts, ms, Ri_sqrts)
stop = time.time()
print("Time per iter: {:.4f}".format((stop - start) / N_iter))
# Compare to Kalman Filter
mu_init = np.zeros(D)
sigma_init = np.eye(D)
Bs = np.ones((D, 1))
sigma_states = np.linalg.inv(Qis)
Cs = np.eye(D)
Ds = np.zeros((D, 1))
sigma_obs = np.linalg.inv(Ris)
inputs = bs
data = ms
print("Timing PyLDS message passing (kalman_filter)")
start = time.time()
for itr in range(N_iter):
kalman_filter(mu_init, sigma_init,
np.concatenate([As, np.eye(D)[None, :, :]]), Bs, np.concatenate([sigma_states, np.eye(D)[None, :, :]]),
Cs, Ds, sigma_obs, inputs, data)
stop = time.time()
print("Time per iter: {:.4f}".format((stop - start) / N_iter))
# Info form comparison
J_init = np.zeros((D, D))
h_init = np.zeros(D)
log_Z_init = 0
J_diag, J_lower_diag, h = convert_lds_to_block_tridiag(As, bs, Qi_sqrts, ms, Ri_sqrts)
J_pair_21 = J_lower_diag
J_pair_22 = J_diag[1:]
J_pair_11 = J_diag[:-1]
J_pair_11[1:] = 0
h_pair_2 = h[1:]
h_pair_1 = h[:-1]
h_pair_1[1:] = 0
log_Z_pair = 0
J_node = np.zeros((T, D, D))
h_node = np.zeros((T, D))
log_Z_node = 0
print("Timing PyLDS message passing (kalman_info_filter)")
start = time.time()
for itr in range(N_iter):
kalman_info_filter(J_init, h_init, log_Z_init,
J_pair_11, J_pair_21, J_pair_22, h_pair_1, h_pair_2, log_Z_pair,
J_node, h_node, log_Z_node)
stop = time.time()
print("Time per iter: {:.4f}".format((stop - start) / N_iter))