# diagonal Gaussian as a special case.
observations = [
"diagonal_gaussian", "gaussian", "diagonal_t", "studentst", "diagonal_ar",
"ar", "diagonal_robust_ar", "robust_ar"
]
# Fit with both SGD and EM
methods = ["sgd", "em"]
results = {}
for obs in observations:
for method in methods:
print("Fitting {} HMM with {}".format(obs, method))
model = HMM(K, D, observations=obs)
train_lls = model.fit(y, method=method)
test_ll = model.log_likelihood(y_test)
smoothed_y = model.smooth(y)
# Permute to match the true states
model.permute(find_permutation(z, model.most_likely_states(y)))
smoothed_z = model.most_likely_states(y)
results[(obs, method)] = (model, train_lls, test_ll, smoothed_z,
smoothed_y)
# Plot the inferred states
fig, axs = plt.subplots(len(observations) + 1, 1, figsize=(12, 8))
# Plot the true states
plt.sca(axs[0])
plt.imshow(z[None, :], aspect="auto", cmap="jet")
plt.title("true")
print("Fitting Gaussian HMM with EM")
hmm = HMM(K, D, observations="gaussian")
hmm_em_lls = hmm.fit(y, method="em", num_em_iters=N_em_iters)
# Plot log likelihoods (fit model is typically better)
plt.figure()
plt.plot(hsmm_em_lls, ls='-', label="HSMM (EM)")
plt.plot(hmm_em_lls, ls='-', label="HMM (EM)")
plt.plot(true_ll * np.ones(N_em_iters), ':', label="true")
plt.legend(loc="lower right")
# Print the test likelihoods (true model is typically better)
print("Test log likelihood")
print("True HSMM: ", true_hsmm.log_likelihood(y_test))
print("Fit HSMM: ", hsmm.log_likelihood(y_test))
print("Fit HMM: ", hmm.log_likelihood(y_test))
# Plot the true and inferred states
hsmm.permute(find_permutation(z, hsmm.most_likely_states(y)))
hsmm_z = hsmm.most_likely_states(y)
hmm.permute(find_permutation(z, hmm.most_likely_states(y)))
hmm_z = hsmm.most_likely_states(y)
# Plot the true and inferred discrete states
plt.figure(figsize=(8, 6))
plt.subplot(311)
plt.imshow(z[None, :1000], aspect="auto", cmap="cubehelix", vmin=0, vmax=K-1)
plt.xlim(0, 1000)
plt.ylabel("True $z")
plt.yticks([])