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))