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")
plt.xticks()
# Make an HMM with the true parameters
true_hmm = HMM(K, D, observations="gaussian")
z, y = true_hmm.sample(T)
z_test, y_test = true_hmm.sample(T)
true_ll = true_hmm.log_probability(y)
# Fit models
N_sgd_iters = 1000
N_em_iters = 100
print("Fitting HMM with SGD")
hmm = HMM(K, D, observations="gaussian")
hmm_sgd_lls = hmm.fit(y, method="sgd", num_iters=N_sgd_iters)
hmm_sgd_test_ll = hmm.log_probability(y_test)
hmm_sgd_smooth = hmm.smooth(y)
print("Fitting HMM with EM")
hmm = HMM(K, D, observations="gaussian")
hmm_em_lls = hmm.fit(y, method="em", num_em_iters=N_em_iters)
hmm_em_test_ll = hmm.log_probability(y_test)
hmm_em_smooth = hmm.smooth(y)
print("Fitting Student's t HMM with SGD")
thmm = HMM(K, D, observations="studentst")
thmm_sgd_lls = thmm.fit(y, method="sgd", num_iters=N_sgd_iters)
thmm_sgd_test_ll = thmm.log_probability(y_test)
thmm_sgd_smooth = thmm.smooth(y)
print("Fitting Student's t HMM with EM")
thmm = HMM(K, D, observations="studentst")
plt.imshow(z[None, :], aspect="auto", cmap=cmap, vmin=0, vmax=len(colors) - 1)
plt.xlim(0, T)
plt.ylabel("$z_{\\mathrm{true}}$")
plt.yticks([])
plt.subplot(212)
plt.imshow(hmm_z[None, :],
aspect="auto",
cmap=cmap,
vmin=0,
vmax=len(colors) - 1)
plt.xlim(0, T)
plt.ylabel("$z_{\\mathrm{inferred}}$")
plt.yticks([])
plt.xlabel("time")
plt.tight_layout()
# In[34]:
# Use the HMM to "smooth" the data
hmm_y = hmm.smooth(y)
plt.figure(figsize=(8, 4))
plt.plot(y + 3 * np.arange(D), '-k', lw=2)
plt.plot(hmm_y + 3 * np.arange(D), '-', lw=2)
plt.xlim(0, T)
plt.ylabel("$y$")
# plt.yticks([])
plt.xlabel("time")
