# In[7]:
N_iters = 50
hmm = HMM(K, D, observations="gaussian")
hmm_lls = hmm.fit(y, method="em", num_em_iters=N_iters, verbose=True)
plt.plot(hmm_lls, label="EM")
plt.plot([0, N_iters], true_ll * np.ones(2), ':k', label="True")
plt.xlabel("EM Iteration")
plt.ylabel("Log Probability")
plt.legend(loc="lower right")
# In[8]:
# Find a permutation of the states that best matches the true and inferred states
hmm.permute(find_permutation(z, hmm.most_likely_states(y)))
# In[11]:
# Plot the true and inferred discrete states
hmm_z = hmm.most_likely_states(y)
plt.figure(figsize=(8, 4))
plt.subplot(211)
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, :],
]
# 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()
# Plot the inferred states
for i, obs in enumerate(observations):
# Now create a new HMM and fit it to the data with EM
N_iters = 50
hmm = HMM(K, D, M,
observations="categorical", observation_kwargs=dict(C=C),
transitions="inputdriven")
# Fit
hmm_lps = hmm.fit(y, inputs=inpt, method="em", num_em_iters=N_iters)
# In[5]:
# Find a permutation of the states that best matches the true and inferred states
hmm.permute(find_permutation(z, hmm.most_likely_states(y, input=inpt)))
z_inf = hmm.most_likely_states(y, input=inpt)
# In[6]:
# Plot the log probabilities of the true and fit models
plt.plot(hmm_lps, label="EM")
plt.plot([0, N_iters], true_lp * np.ones(2), ':k', label="True")
plt.legend(loc="lower right")
plt.xlabel("EM Iteration")
plt.xlim(0, N_iters)
plt.ylabel("Log Probability")
