def test_hmm_likelihood(T=500, 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 pyhsmm.basic.distributions import Gaussian
hmm = OldHMM(
[Gaussian(mu=C[k], sigma=sigma * np.eye(D)) for k in range(K)],
trans_matrix=A,
init_state_distn="uniform")
true_lkhd = hmm.log_likelihood(y)
# Make an HMM with these parameters
hmm = HMM(K, D, observations="gaussian")
hmm.transitions.log_Ps = np.log(A)
hmm.observations.mus = C
hmm.observations.inv_sigmas = np.log(sigma) * np.ones((K, D))
test_lkhd = hmm.log_probability(y)
assert np.allclose(true_lkhd, test_lkhd)
def test_viterbi(T=1000, K=20, 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 pyhsmm.basic.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")
oldhmm.add_data(y)
states = oldhmm.states_list.pop()
states.Viterbi()
z_star = states.stateseq
# Make an HMM with these parameters
hmm = ssm.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))
z_star2 = hmm.most_likely_states(y)
assert np.allclose(z_star, z_star2)
def test_hmm_likelihood_perf(T=10000, K=50, D=20):
# 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")
states = oldhmm.add_data(y)
tic = time()
true_lkhd = states.log_likelihood()
pyhsmm_dt = time() - tic
print("PyHSMM: ", pyhsmm_dt, "sec. Val: ", true_lkhd)
# Make an HMM with these parameters
hmm = ssm.HMM(K, D, observations="gaussian")
hmm.transitions.log_Ps = np.log(A)
hmm.observations.mus = C
hmm.observations._sqrt_Sigmas = np.sqrt(sigma) * np.array(
[np.eye(D) for k in range(K)])
tic = time()
test_lkhd = hmm.log_probability(y)
smm_dt = time() - tic
print("SMM HMM: ", smm_dt, "sec. Val: ", test_lkhd)
# Make an ARHMM with these parameters
arhmm = ssm.HMM(K, D, observations="ar")
tic = time()
arhmm.log_probability(y)
arhmm_dt = time() - tic
print("SSM ARHMM: ", arhmm_dt, "sec.")
# Make an ARHMM with these parameters
arhmm = ssm.HMM(K, D, observations="ar")
tic = time()
arhmm.expected_states(y)
arhmm_dt = time() - tic
print("SSM ARHMM Expectations: ", arhmm_dt, "sec.")
def test_expectations(T=1000, K=20, 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 pyhsmm.basic.distributions import Gaussian
hmm = OldHMM(
[Gaussian(mu=C[k], sigma=sigma * np.eye(D)) for k in range(K)],
trans_matrix=A,
init_state_distn="uniform")
hmm.add_data(y)
states = hmm.states_list.pop()
states.E_step()
true_Ez = states.expected_states
true_E_trans = states.expected_transcounts
# Make an HMM with these parameters
hmm = HMM(K, D, observations="gaussian")
hmm.transitions.log_Ps = np.log(A)
hmm.observations.mus = C
hmm.observations.inv_sigmas = np.log(sigma) * np.ones((K, D))
test_Ez, test_Ezzp1, _ = hmm.expected_states(y)
test_E_trans = test_Ezzp1.sum(0)
print(true_E_trans.round(3))
print(test_E_trans.round(3))
assert np.allclose(true_Ez, test_Ez)
assert np.allclose(true_E_trans, test_E_trans)
def run_HMM(time_series, **kwargs):
# Directly use knowledge of the number of modes
K = kwargs['num_gt_labels']
D_obs = kwargs['data_dim']
obs_hypparams = {
'mu_0': np.zeros(D_obs),
'sigma_0': np.eye(D_obs),
'kappa_0': 0.10,
'nu_0': D_obs + 2
}
obs_distns = [
pyhsmm.distributions.Gaussian(**obs_hypparams) for _ in range(K)
]
hmm = HMM(alpha=kwargs['alpha'],
init_state_concentration=kwargs['init_state_concentration'],
obs_distns=obs_distns)
return inference(time_series, hmm, **kwargs)
init_state_concentration=10.,
alpha=6.,gamma=6.,
obs_distns=GMMs,
dur_distns=true_dur_distns)
data, truelabels = truemodel.generate(1000)
#################
# remove data #
#################
# using an HMM of course
deletion_hmm = HMM(
init_state_concentration=10.,
alpha=6.,gamma=6.,
obs_distns=GMMs[:2], # placeholders, not really used
)
_, todelete = deletion_hmm.generate(data.shape[0])
data[todelete == 0] == np.nan
#####################################
# set up FrozenMixture components #
#####################################
# list of all Gaussians
component_library = [c for m in GMMs for c in m.components]
library_size = len(component_library)
alpha=6.,
gamma=6.,
obs_distns=GMMs,
dur_distns=true_dur_distns)
data, truelabels = truemodel.generate(1000)
#################
# remove data #
#################
# using an HMM of course
deletion_hmm = HMM(
init_state_concentration=10.,
alpha=6.,
gamma=6.,
obs_distns=GMMs[:2], # placeholders, not really used
)
_, todelete = deletion_hmm.generate(data.shape[0])
data[todelete == 0] == np.nan
#####################################
# set up FrozenMixture components #
#####################################
# list of all Gaussians
component_library = [c for m in GMMs for c in m.components]
library_size = len(component_library)
