def test_hmm_likelihood(T=1000, K=5, D=2):
# Create a true HMM
A = npr.rand(K, K)
A /= A.sum(axis=1, keepdims=True)
A = 0.75 * np.eye(K) + 0.25 * A
C = npr.randn(K, D)
sigma = 0.01
# Sample from the true HMM
z = np.zeros(T, dtype=int)
y = np.zeros((T, D))
for t in range(T):
if t > 0:
z[t] = np.random.choice(K, p=A[z[t - 1]])
y[t] = C[z[t]] + np.sqrt(sigma) * npr.randn(D)
# Compare to pyhsmm answer
from pyhsmm.models import HMM as OldHMM
from pybasicbayes.distributions import Gaussian
oldhmm = OldHMM(
[Gaussian(mu=C[k], sigma=sigma * np.eye(D)) for k in range(K)],
trans_matrix=A,
init_state_distn="uniform")
true_lkhd = oldhmm.log_likelihood(y)
# Make an HMM with these parameters
hmm = HMM(K, D, observations="diagonal_gaussian")
hmm.transitions.log_Ps = np.log(A)
hmm.observations.mus = C
hmm.observations.sigmasq = sigma * np.ones((K, D))
test_lkhd = hmm.log_probability(y)
assert np.allclose(true_lkhd, test_lkhd)
import matplotlib
import matplotlib.pyplot as plt
from ssm.models import HMM
# Set the parameters of the HMM
T = 500 # number of time bins
K = 5 # number of discrete states
D = 2 # number of observed dimensions
# 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)
import matplotlib
import matplotlib.pyplot as plt
from ssm.models import HMM
from ssm.util import find_permutation
# Set the parameters of the HMM
T = 500 # number of time bins
K = 5 # number of discrete states
D = 2 # number of observed dimensions
# Make an HMM with the true parameters
true_hmm = HMM(K, D, observations="diagonal_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
# A bunch of observation models that all include the
# 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"]
# Make an HMM
true_hmm = HMM(K, D, M,
observations="categorical", observation_kwargs=dict(C=C),
transitions="inputdriven")
# Optionally, turn up the input weights to exaggerate the effect
# true_hmm.transitions.Ws *= 3
# Create an exogenous input
inpt = np.sin(2 * np.pi * np.arange(T) / 50)[:, None] + 1e-1 * npr.randn(T, M)
# Sample some data from the HMM
z, y = true_hmm.sample(T, input=inpt)
# Compute the true log probability of the data, summing out the discrete states
true_lp = true_hmm.log_probability(y, inputs=inpt)
# In[3]:
# Plot the data
plt.figure(figsize=(8, 5))
plt.subplot(311)
plt.plot(inpt)
plt.xticks([])
plt.xlim(0, T)
plt.ylabel("input")
plt.subplot(312)
