def test_reset(self):
m = ConvergenceMonitor(tol=1e-3, n_iter=10, verbose=False)
m.iter = 1
m.history.append(-0.01)
m._reset()
assert m.iter == 0
assert not m.history
def test_report_first_iteration(self, capsys):
m = ConvergenceMonitor(tol=1e-3, n_iter=10, verbose=True)
m.report(-0.01)
out, err = capsys.readouterr()
assert not out
expected = m._template.format(iter=1, logprob=-0.01, delta=np.nan)
assert err.splitlines() == [expected]
def test_report_first_iteration(self, capsys):
m = ConvergenceMonitor(tol=1e-3, n_iter=10, verbose=True)
m.report(-0.01)
out, err = capsys.readouterr()
assert not out
expected = m._template.format(iter=1, logprob=-0.01, delta=float("nan"))
assert err.splitlines() == [expected]
def test_converged_by_iterations(self):
m = ConvergenceMonitor(tol=1e-3, n_iter=2, verbose=False)
assert not m.converged
m.report(-0.01)
assert not m.converged
m.report(-0.1)
assert m.converged
def test_reset(self):
m = ConvergenceMonitor(tol=1e-3, n_iter=10, verbose=False)
m.iter = 1
m.history.append(-0.01)
m._reset()
assert m.iter == 0
assert not m.history
def fit(self, X, lengths=None):
X = check_array(X)
self._init(X, lengths=lengths)
self._check()
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, self.verbose)
for iter in range(self.n_iter):
stats = self._initialize_sufficient_statistics()
curr_logprob = 0
framelogprob = self._compute_log_likelihood(X)
logprob, fwdlattice = self._do_forward_pass(framelogprob)
curr_logprob += logprob
bwdlattice = self._do_backward_pass(framelogprob)
posteriors = self._compute_posteriors(fwdlattice, bwdlattice)
self._accumulate_sufficient_statistics(
stats, X, framelogprob, posteriors, fwdlattice,
bwdlattice)
# XXX must be before convergence check, because otherwise
# there won't be any updates for the case ``n_iter=1``.
self._do_mstep(stats)
self.monitor_.report(curr_logprob)
if self.monitor_.converged:
self.framelogprob = framelogprob
break
return self
def test_converged_by_logprob(self):
m = ConvergenceMonitor(tol=1e-3, n_iter=10, verbose=False)
for logprob in [-0.03, -0.02, -0.01]:
m.report(logprob)
assert not m.converged
m.report(-0.0101)
assert m.converged
def fit(self, X, lengths=None):
"""Estimate model parameters.
An initialization step is performed before entering the
EM algorithm. If you want to avoid this step for a subset of
the parameters, pass proper ``init_params`` keyword argument
to estimator's constructor.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Feature matrix of individual samples.
lengths : array-like of integers, shape (n_sequences, )
Lengths of the individual sequences in ``X``. The sum of
these should be ``n_samples``.
Returns
-------
self : object
Returns self.
"""
X = check_array(X)
self._init(X, lengths=lengths)
self._check()
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, self.verbose)
for iter in range(self.n_iter):
stats = self._initialize_sufficient_statistics()
curr_logprob = 0
for i, j in iter_from_X_lengths(X, lengths):
framelogprob = self._compute_log_likelihood(X[i:j])
logprob, fwdlattice = self._do_forward_pass(framelogprob)
curr_logprob += logprob
bwdlattice = self._do_backward_pass(framelogprob)
posteriors = self._compute_posteriors(fwdlattice, bwdlattice)
# fix posteriors
if self.states_prior is not None and self.fp_state is not None:
for k in range(len(self.states_prior)):
if self.states_prior[k] == 0:
# non footprint states
posteriors[k][self.fp_state] = 0.0
posteriors[k] = posteriors[k] / sum(posteriors[k])
elif self.states_prior[k] == 1:
# footprint states
posteriors[k] = 0.0 / sum(posteriors[k])
posteriors[k][self.fp_state] = 1.0
self._accumulate_sufficient_statistics(stats, X[i:j],
framelogprob,
posteriors, fwdlattice,
bwdlattice)
self._do_mstep(stats)
self.monitor_.report(curr_logprob)
if self.monitor_.converged:
break
return self
def test_report(self, capsys):
n_iter = 10
m = ConvergenceMonitor(tol=1e-3, n_iter=n_iter, verbose=True)
for i in reversed(range(n_iter)):
m.report(-0.01 * i)
out, err = capsys.readouterr()
assert not out
assert len(err.splitlines()) == n_iter
def test_report(self, capsys):
n_iter = 10
m = ConvergenceMonitor(tol=1e-3, n_iter=n_iter, verbose=True)
for i in reversed(range(n_iter)):
m.report(-0.01 * i)
out, err = capsys.readouterr()
assert not out
assert len(err.splitlines()) == n_iter
def __init__(self, config: dict):
if "tol" in config["train"] and isinstance(config["train"]["tol"],
str):
config["train"]["tol"] = {
"-inf": -np.inf,
"inf": np.inf
}[config["train"]["tol"]]
self.gmm_hmm = _GMMHMM(**config["parameters"])
self.gmm_hmm.monitor_ = ConvergenceMonitor(*(config["train"][key]
for key in ("tol",
"n_iter",
"verbose")))
self.iepoch = 1
self.rand_inits = (config["train"].get("weight_rand_init", 0),
config["train"].get("mean_rand_init", 0),
config["train"].get("covar_rand_init", 0))
self.limit_inits = (
config["train"].get("weight_min_init", 0),
config["train"].get("covar_min_init", 0),
)
self.rescale = config["train"].get("rescale_samples", False)
if self.rescale:
self.means = None
self.stddevs = None
def fit(self, X, lengths=None):
"""Estimate model parameters.
An initialization step is performed before entering the
EM algorithm. If you want to avoid this step for a subset of
the parameters, pass proper ``init_params`` keyword argument
to estimator's constructor.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Feature matrix of individual samples.
lengths : array-like of integers, shape (n_sequences, )
Lengths of the individual sequences in ``X``. The sum of
these should be ``n_samples``.
Returns
-------
self : object
Returns self.
"""
X = check_array(X)
self._init(X, lengths=lengths)
self._check()
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, self.verbose)
for iter in range(self.n_iter):
stats = self._initialize_sufficient_statistics()
curr_logprob = 0
for i, j in iter_from_X_lengths(X, lengths):
framelogprob = self._compute_log_likelihood(X[i:j])
logprob, fwdlattice = self._do_forward_pass(framelogprob)
curr_logprob += logprob
bwdlattice = self._do_backward_pass(framelogprob)
posteriors = self._compute_posteriors(fwdlattice, bwdlattice)
# fix posteriors
if self.states_prior is not None and self.fp_state is not None:
for k in range(len(self.states_prior)):
if self.states_prior[k] == 0:
# non footprint states
posteriors[k][self.fp_state] = 0.0
posteriors[k] = posteriors[k] / sum(posteriors[k])
elif self.states_prior[k] == 1:
# footprint states
posteriors[k] = 0.0 / sum(posteriors[k])
posteriors[k][self.fp_state] = 1.0
self._accumulate_sufficient_statistics(stats, X[i:j], framelogprob, posteriors, fwdlattice, bwdlattice)
self._do_mstep(stats)
self.monitor_.report(curr_logprob)
if self.monitor_.converged:
break
return self
def test_converged_by_iterations(self):
m = ConvergenceMonitor(tol=1e-3, n_iter=2, verbose=False)
assert not m.converged
m.report(-0.01)
assert not m.converged
m.report(-0.1)
assert m.converged
def test_converged_by_logprob(self):
m = ConvergenceMonitor(tol=1e-3, n_iter=10, verbose=False)
for logprob in [-0.03, -0.02, -0.01]:
m.report(logprob)
assert not m.converged
m.report(-0.0101)
assert m.converged
class PoissonHMM(_BaseHMM):
# Overriding the parent
def __init__(self, framelogprob, rates, M, *args, **kwargs):
_BaseHMM.__init__(self, *args, **kwargs)
# rates for each state
self.rates = rates
self.M = M
self.framelogprob = framelogprob
def _compute_log_likelihood(self, X):
J, M, N = self.n_components, X.shape[1], X.shape[0]
observation_prob = np.zeros((M, J))
for m in range(M):
for j in range(J):
for n in range(N):
observation_prob[m, j] += poisson.logpmf(X[n, m], self.rates[j])
o = observation_prob - logsumexp(observation_prob, axis=0)
extra_normalized = o - np.amax(o, axis=1)[:, np.newaxis]
return extra_normalized
def _initialize_sufficient_statistics(self):
stats = super(PoissonHMM, self)._initialize_sufficient_statistics()
stats['post'] = np.zeros(1)
stats['obs'] = np.zeros((self.M))
return stats
def _accumulate_sufficient_statistics(self, stats, obs, framelogprob, posteriors, fwdlattice, bwdlattice):
super(PoissonHMM, self)._accumulate_sufficient_statistics(
stats, obs, framelogprob, posteriors, fwdlattice, bwdlattice)
M = len(stats['obs'])
post = np.zeros((M))
J = len(posteriors[0, :])
for j in range(J):
state = j + 1
post += posteriors[:,j] * state
stats['post'] += np.sum(post)
for o in obs:
stats['obs'] += o
def fit(self, X, lengths=None):
X = check_array(X)
self._init(X, lengths=lengths)
self._check()
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, self.verbose)
for iter in range(self.n_iter):
stats = self._initialize_sufficient_statistics()
curr_logprob = 0
framelogprob = self._compute_log_likelihood(X)
logprob, fwdlattice = self._do_forward_pass(framelogprob)
curr_logprob += logprob
bwdlattice = self._do_backward_pass(framelogprob)
posteriors = self._compute_posteriors(fwdlattice, bwdlattice)
self._accumulate_sufficient_statistics(
stats, X, framelogprob, posteriors, fwdlattice,
bwdlattice)
# XXX must be before convergence check, because otherwise
# there won't be any updates for the case ``n_iter=1``.
self._do_mstep(stats)
self.monitor_.report(curr_logprob)
if self.monitor_.converged:
self.framelogprob = framelogprob
break
return self
def _do_mstep(self, stats):
super(PoissonHMM, self)._do_mstep(stats)
denom = stats['post']
nom = np.sum(stats['obs'])
J = len(self.rates)
rate = nom / denom
self.rates = [rate * j for j in range(1, J+1)]
class SemiSupervisedGaussianHMM(GaussianHMM):
def __init__(self,
n_components=1,
covariance_type='diag',
min_covar=1e-3,
startprob_prior=1.0,
transmat_prior=1.0,
means_prior=0,
means_weight=0,
covars_prior=1e-2,
covars_weight=1,
algorithm="viterbi",
random_state=None,
n_iter=5,
tol=1e-2,
verbose=False,
params="stmc",
init_params="stmc",
states_prior=None,
fp_state=None):
GaussianHMM.__init__(self,
n_components=n_components,
covariance_type=covariance_type,
min_covar=min_covar,
startprob_prior=startprob_prior,
transmat_prior=transmat_prior,
means_prior=means_prior,
means_weight=means_weight,
covars_prior=covars_prior,
covars_weight=covars_weight,
algorithm=algorithm,
random_state=random_state,
n_iter=n_iter,
tol=tol,
verbose=verbose,
params=params,
init_params=init_params)
self.covariance_type = covariance_type
self.min_covar = min_covar
self.means_prior = means_prior
self.means_weight = means_weight
self.covars_prior = covars_prior
self.covars_weight = covars_weight
self.states_prior = states_prior
self.fp_state = fp_state
def fit(self, X, lengths=None):
"""Estimate model parameters.
An initialization step is performed before entering the
EM algorithm. If you want to avoid this step for a subset of
the parameters, pass proper ``init_params`` keyword argument
to estimator's constructor.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Feature matrix of individual samples.
lengths : array-like of integers, shape (n_sequences, )
Lengths of the individual sequences in ``X``. The sum of
these should be ``n_samples``.
Returns
-------
self : object
Returns self.
"""
X = check_array(X)
self._init(X, lengths=lengths)
self._check()
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, self.verbose)
for iter in range(self.n_iter):
stats = self._initialize_sufficient_statistics()
curr_logprob = 0
for i, j in iter_from_X_lengths(X, lengths):
framelogprob = self._compute_log_likelihood(X[i:j])
logprob, fwdlattice = self._do_forward_pass(framelogprob)
curr_logprob += logprob
bwdlattice = self._do_backward_pass(framelogprob)
posteriors = self._compute_posteriors(fwdlattice, bwdlattice)
# fix posteriors
if self.states_prior is not None and self.fp_state is not None:
for k in range(len(self.states_prior)):
if self.states_prior[k] == 0:
# non footprint states
posteriors[k][self.fp_state] = 0.0
posteriors[k] = posteriors[k] / sum(posteriors[k])
elif self.states_prior[k] == 1:
# footprint states
posteriors[k] = 0.0 / sum(posteriors[k])
posteriors[k][self.fp_state] = 1.0
self._accumulate_sufficient_statistics(stats, X[i:j],
framelogprob,
posteriors, fwdlattice,
bwdlattice)
self._do_mstep(stats)
self.monitor_.report(curr_logprob)
if self.monitor_.converged:
break
return self
class SpaMHMM(BaseEstimator):
def __init__(self,
n_nodes,
mix_dim,
n_components,
n_features,
graph=None,
emission='gaussian',
n_iter=10,
tol=1e-2,
n_iter_mstep=100,
lr_mstep=1e-3,
rho1=0.9,
rho2=0.99,
verbose=False,
name='spamhmm'):
super(SpaMHMM, self).__init__()
self.n_nodes = n_nodes
self.mix_dim = mix_dim
self.n_components = n_components
self.n_features = n_features
self.graph = graph
self.emission = emission
self.n_iter = n_iter
self.tol = tol
self.n_iter_mstep = n_iter_mstep
self.lr_mstep = lr_mstep
self.rho1 = rho1
self.rho2 = rho2
self.verbose = verbose
self.name = name
def init_params(self, X):
'''
Parameters initialization.
'''
if type(X) == list:
X = np.concatenate(X)
self.mixCoefUnNorm = np.random.rand(self.n_nodes, self.mix_dim) + 1e-9
self.mixCoef = np.reshape(
np.ones(3) * (1 / 3),
(1, 3)) #relu_normalization(self.mixCoefUnNorm, axis=1) # #
startProb = np.exp(np.random.randn(self.mix_dim, self.n_components))
normalize(startProb, axis=1)
transProb = np.exp(
np.random.randn(self.mix_dim, self.n_components,
self.n_components))
normalize(transProb, axis=2)
self.time_ = 1
self.first_moment_ = np.zeros_like(self.mixCoef)
self.second_moment_ = np.zeros_like(self.mixCoef)
if self.emission == 'gaussian':
self.mixModels = [
hmm.GaussianHMM(n_components=self.n_components,
covariance_type='diag')
for i in range(self.mix_dim)
]
for m in range(self.mix_dim):
self.mixModels[m]._init(X)
seed = 1
trans = rand_initialization.generate_transitions_random(
seed, 3, self.n_components, .1)
self.mixModels[0].transmat_ = trans[0]
self.mixModels[1].transmat_ = trans[1]
self.mixModels[2].transmat_ = trans[2]
else:
raise NotImplementedError('{} emission is not implemented'.format(
self.emission))
def scores_per_seq(self, X, y, lengths=None):
'''
Computes the log-likelihood for each sequence in X coming from nodes y.
Inputs:
X - np.array of size (n_samples, n_features).
y - np.int of size n_sequences, whose entries are in the range
[0, n_nodes-1].
lengths - list containing the lengths of each individual sequence
in X, with size n_sequences.
Outputs:
log_likelihood - np.array of size n_sequences.
'''
if type(X) == list:
lengths = [x.shape[0] for x in X]
X = np.concatenate(X)
y = np.array(y)
N = y.shape[0]
log_likelihood = np.zeros(N)
for seq_idx, (i, j) in enumerate(iter_from_X_lengths(X, lengths)):
ll_per_comp = np.zeros(self.mix_dim)
for m in range(self.mix_dim):
if self.mixCoef[y[seq_idx], m] == 0.:
continue
ll_per_comp[m] = self.mixModels[m].score(X[i:j, :])
nonzero_idx = (self.mixCoef[y[seq_idx], :] != 0.)
log_likelihood[seq_idx] = logsumexp(
np.log(self.mixCoef[y[seq_idx], nonzero_idx]) +
ll_per_comp[nonzero_idx])
return log_likelihood
def score(self, X, y, lengths=None):
'''
Computes the mean log-likelihood for sequences in X coming from
nodes y.
Inputs:
X - np.array of size (n_samples, n_features).
y - np.int of size n_sequences, whose entries are in the
range [0, n_nodes-1].
lengths - list containing the lengths of each individual sequence
in X, with size n_sequences.
Outputs:
log_likelihood - scalar.
'''
if type(X) == list:
lengths = [x.shape[0] for x in X]
X = np.concatenate(X)
y = np.array(y)
self._check()
Nsamples = X.shape[0]
log_likelihood = np.sum(self.scores_per_seq(X, y, lengths))
return log_likelihood / Nsamples
def _check(self):
'''
Validates mixCoef parameter. The remaining parameters are validated
by the hmm.check() routine.
Raises
------
ValueError
If mixCoef have an invalid shape or do not sum to 1.
'''
if self.mixCoef.shape != (self.n_nodes, self.mix_dim):
raise ValueError('mixCoef must have length n_components')
if not np.allclose(self.mixCoef.sum(axis=1), 1.0):
raise ValueError('mixCoef must sum to 1.0 (got {0:.4f})'.format(
self.mixCoef.sum(axis=1)))
def _compute_mixture_posteriors(self, X, y, lengths):
'''
Computes the posterior log-probability of each mixture component given
the observations X, y.
Inputs:
X - np.array of size (n_samples, n_features).
y - np.int of size n_sequences, whose entries are in the
range [0, n_nodes-1].
lengths - list containing the lengths of each individual sequence
in X, with size n_sequences.
Outputs:
logmixpost - np.array of size (n_sequences, mix_dim).
'''
N = len(lengths)
transitions = []
#means = []
logmixpost = np.zeros((N, self.mix_dim))
for m in range(self.mix_dim):
ll_m = np.zeros(N)
for seq_idx, (i, j) in enumerate(iter_from_X_lengths(X, lengths)):
ll_m[seq_idx] = self.mixModels[m].score(X[i:j, :])
transitions = np.append(transitions, self.mixModels[m].transmat_)
#means = np.append(means, self.mixModels[m].means_)
logmixpost[:, m] = ll_m + np.log(self.mixCoef[y, m] + .000000001)
log_normalize(logmixpost, axis=1)
return logmixpost, transitions #, means
def _compute_sufficient_statistics_in_mix_comp(self, X, y, lengths,
logmixpost, stats):
'''
Accumulates sufficient statistics for the parameters of each HMM in the
mixture.
Inputs:
X - np.array of size (n_samples, n_features).
y - np.int of size n_sequences, whose entries are in the
range [0, n_nodes-1].
lengths - list containing the lengths of each individual sequence
in X, with size n_sequences.
logmixpost - np.array of size (n_sequences, mix_dim).
stats - dictionary containing sufficient statistics (changed
inplace).
'''
for m in range(self.mix_dim):
for seq_idx, (i, j) in enumerate(iter_from_X_lengths(X, lengths)):
if self.mixCoef[y[seq_idx], m] == 0.:
continue
framelogprob = self.mixModels[m]._compute_log_likelihood(
X[i:j, :])
_, fwdlattice = (
self.mixModels[m]._do_forward_pass(framelogprob))
bwdlattice = self.mixModels[m]._do_backward_pass(framelogprob)
posteriors = self.mixModels[m]._compute_posteriors(
fwdlattice, bwdlattice)
fwdlattice += logmixpost[seq_idx, m]
bwdlattice += logmixpost[seq_idx, m]
posteriors *= np.exp(logmixpost[seq_idx, m])
self.mixModels[m]._accumulate_sufficient_statistics(
stats['mix_idx' + str(m)], X[i:j, :], framelogprob,
posteriors, fwdlattice, bwdlattice)
def _compute_sufficient_statistics(self, X, y, lengths):
'''
Computes sufficient statistics to be used in the M-step.
Inputs:
X - np.array of size (n_samples, n_features).
y - np.int of size n_sequences, whose entries are in the
range [0, n_nodes-1].
lengths - list containing the lengths of each individual sequence
in X, with size n_sequences.
Outputs:
stats - dictionary containing sufficient statistics.
'''
def check_large_diff(rates):
return abs(rates[0] - rates[1]) == np.max(
abs(rates[0] - rates[1])) #>= .9 #10
def get_index_of_large_diff(rates):
which_cluster = 0
if (rates[0] - rates[1]).any() < 0:
which_cluster = 1
return which_cluster, np.where(
abs(rates[0] -
rates[1]) == np.max(abs(rates[0] - rates[1])))[0][
0] # np.where(abs(rates[0] - rates[1]) >= .9)[0][0]
means = np.zeros((self.mix_dim, self.mixModels[0].n_components))
for m in range(self.mix_dim):
means[m] = self.mixModels[m].means_.flatten()
i = self.n_components # some init value so that it never collides with possible indexes of the arrays
greater_cluster = 0
if check_large_diff(means).any():
greater_cluster, i = get_index_of_large_diff(means)
stats = {'mix_post': np.zeros((self.n_nodes, self.mix_dim))}
for m in range(self.mix_dim):
stats['mix_idx' + str(m)] = (
self.mixModels[m]._initialize_sufficient_statistics())
stats['trans_prior' + str(m)] = np.ones(
(self.n_components, self.n_components))
print(means[m])
logmixpost, trans = self._compute_mixture_posteriors(X, y, lengths)
for k in range(self.n_nodes):
stats['mix_post'][k, :] = np.sum(np.exp(logmixpost[y == k, :]),
axis=0)
logmixpost -= np.amax(logmixpost, axis=0).reshape(1, self.mix_dim)
self._compute_sufficient_statistics_in_mix_comp(
X, y, lengths, logmixpost, stats)
if self.reg_:
stats['n_seqs_per_node'] = np.zeros(self.n_nodes)
for k in range(self.n_nodes):
stats['n_seqs_per_node'][k] = np.sum(y == k)
return stats
def _fit_coef(self, stats):
'''
Performs the M step of the EM algorithm for the mixture coefficients,
via gradient ascent. This function is used only when a graph is given.
Inputs:
stats - dictionary containing sufficient statistics.
n_iter - number of update iterations.
'''
Nseqs = np.sum(stats['n_seqs_per_node'])
for it in range(self.n_iter_mstep):
grad = np.zeros_like(self.mixCoefUnNorm)
post_coef_dif = (stats['mix_post'] - self.mixCoef *
(stats['n_seqs_per_node'].reshape(-1, 1)))
G_mixCoef = self.graph @ self.mixCoef
reg_dif = (
self.mixCoef *
(G_mixCoef -
(np.sum(self.mixCoef * G_mixCoef, axis=1).reshape(-1, 1))))
mask = (self.mixCoefUnNorm > 0.)
grad[mask] = (drelu(self.mixCoefUnNorm[mask]) /
relu(self.mixCoefUnNorm[mask]))
grad *= post_coef_dif / Nseqs + reg_dif
self.mixCoefUnNorm = self._adam(self.mixCoefUnNorm, grad)
self.mixCoef = relu_normalization(self.mixCoefUnNorm, axis=1)
def _adam(self, w, dw, delta=1e-8):
'''
Performs an ascending step using the Adam algorithm.
Inputs:
w - np.array, the current value of the parameter.
dw - np.array with the same shape as w, the gradient of the
objective with respect to w.
delta - small constant to avoid division by zero (default: 1e-8)
Outputs:
next_w - np.array with the same shape as w, the updated value of
the parameter.
'''
next_first_moment = self.rho1 * self.first_moment_ + (1 -
self.rho1) * dw
next_second_moment = (self.rho2 * self.second_moment_ +
(1 - self.rho2) * dw**2)
correct_first_moment = next_first_moment / (1 - self.rho1**self.time_)
correct_second_moment = (next_second_moment /
(1 - self.rho2**self.time_))
upd_w = (self.lr_mstep * correct_first_moment /
(np.sqrt(correct_second_moment) + delta))
next_w = w + upd_w
self.time_ += 1
self.first_moment_ = next_first_moment
self.second_moment_ = next_second_moment
return next_w
def _do_mstep(self, stats):
'''
Performs the M step of the EM algorithm, updating all model parameters.
Inputs:
stats - dictionary containing sufficient statistics.
'''
if self.reg_:
self._fit_coef(stats)
else:
self.mixCoef = stats['mix_post']
normalize(self.mixCoef, axis=1)
for m in range(self.mix_dim):
self.mixModels[m].transmat_prior = stats['trans_prior' + str(m)]
self.mixModels[m]._do_mstep(stats['mix_idx' + str(m)])
def fit(self, X, y, lengths=None, valid_data=None):
'''
Trains SpaMHMM on data X, y, using the EM algorithm.
Inputs:
X - np.array of size (n_samples, n_features).
y - np.int of size n_sequences, whose entries are in the
range [0, n_nodes-1].
lengths - list containing the lengths of each individual sequence
in X, with size n_sequences.
valid_data - tuple (X_valid, y_valid, lengths_valid) containing the
validation data; if validation data is given, the
model with the lowest validation loss is saved in a
pickle file (optional, default:None).
'''
if type(X) == list:
lengths = [x.shape[0] for x in X]
X = np.concatenate(X)
y = np.array(y)
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, False)
if valid_data is not None:
X_valid, y_valid, lengths_valid = valid_data
if type(X_valid) == list:
lengths_valid = [x.shape[0] for x in X_valid]
X_valid = np.concatenate(X_valid)
y_valid = np.array(y_valid)
max_validscore = float('-inf')
validloss_hist = []
if self.graph is not None:
self.reg_ = True
else:
self.reg_ = False
self.init_params(X)
self._check()
prevscore = float('-inf')
trainloss_hist = []
for it in range(self.n_iter):
t0 = time.time()
stats = self._compute_sufficient_statistics(X, y, lengths)
self._do_mstep(stats)
print('trans0 {}'.format(self.mixModels[0].transmat_))
print('trans1 {}'.format(self.mixModels[1].transmat_))
t1 = time.time()
currscore = self.score(X, y, lengths)
trainloss_hist.append(-currscore)
if valid_data is not None:
validscore = self.score(X_valid, y_valid, lengths_valid)
validloss_hist.append(-validscore)
if validscore > max_validscore:
max_validscore = validscore
f = open(self.name + '.pkl', 'wb')
pickle.dump(self, f)
if self.verbose:
if (not self.reg_) and (prevscore > currscore):
print(
'WARNING: loss has increased at iteration {}!'.format(
it))
print('prev loss = {:.5f}, curr loss = {:.5f}'.format(
-prevscore, -currscore))
elif valid_data is not None:
print('it {}: train loss = {:.5f}, valid loss = {:.5f}, '
'{:.3f} sec/it'.format(it + 1, -currscore,
-validscore, t1 - t0))
else:
print('it {}: loss = {:.5f}, {:.3f} sec/it'.format(
it + 1, -currscore, t1 - t0))
ll = np.sum(self.scores_per_seq(X, y, lengths))
print("ll: {}".format(ll))
# ll = 0
# for m in range(self.mix_dim):
# ll += np.max(self.mixModels[m]._compute_log_likelihood(X))
self.monitor_.report(currscore)
# self.monitor_.report(ll)
# print("ll: {}".format(ll))
if self.monitor_.converged:
if self.verbose:
print(
'Loss improved less than {}. Training stopped.'.format(
self.tol))
break
prevscore = currscore
if valid_data:
return trainloss_hist, validloss_hist
else:
return trainloss_hist
def predict_next_observ(self, X, y, x_candidates):
'''
Finds the most likely next observation, given the sequence X at node y,
by trying every candidate point in x_candidates.
Inputs:
X - observed sequence, np.array of size (length, n_features).
y - the node index, integer.
x_candidates - candidate points, np.array of size (n_candidates,
n_features).
Outputs:
next_observ - predicted observation, np.array of size n_features.
'''
length = X.shape[0]
Ncand = x_candidates.shape[0]
ll_per_comp_X = np.zeros(self.mix_dim)
ll_per_comp_nxt_obs = np.zeros((Ncand, self.mix_dim))
for m in range(self.mix_dim):
if self.mixCoef[y, m] == 0.:
continue
ll_per_comp_X[m], state_post = self.mixModels[m].score_samples(X)
final_state_post = state_post[length - 1, :]
next_state_logpost = logsumexp(
(np.log(self.mixModels[m].transmat_.T) +
np.log(final_state_post)),
axis=1)
emiss_ll = self.mixModels[m]._compute_log_likelihood(x_candidates)
ll_per_comp_nxt_obs[:, m] = logsumexp(
emiss_ll + (next_state_logpost.reshape(1, -1)), axis=1)
nonzero_idx = (self.mixCoef[y, :] != 0.)
ll_next_observ = logsumexp(
(ll_per_comp_nxt_obs[:, nonzero_idx] + ll_per_comp_X[nonzero_idx] +
np.log(self.mixCoef[y, nonzero_idx])),
axis=1)
max_idx = np.argmax(ll_next_observ)
next_observ = x_candidates[max_idx, :]
return next_observ
def greedy_predict_seq(self, X, y, x_candidates, n_samples):
'''
Finds a greedy approximation of the most likely next n_samples, given
the sequence X at node y, trying every candidate point in x_candidates
for each sample.
Inputs:
X - observed sequence, np.array of size (length, n_features).
y - the node index, integer.
x_candidates - candidate points, np.array of size (n_candidates,
n_features).
Outputs:
Xpred - predicted sequence, np.array of size (n_samples,
n_features).
'''
length = X.shape[0]
Xpred = X
for i in range(n_samples):
next_observ = (self.predict_next_observ(Xpred, y,
x_candidates).reshape(
1, -1))
Xpred = np.concatenate([Xpred, next_observ], axis=0)
return Xpred[length::, :]
def sample(self, y, n_samples, Xpref=None):
'''
Samples a sequence of observations from the MHMM observation
distribution. If a prefix sequence is given, the new sequence is
sampled from the posterior distribution given that prefix sequence.
Inputs:
y - the node index, integer.
n_samples - the number of samples, integer.
Xpref - prefix sequence, np.array of size (pref_len, n_features)
(optional, default: None).
Outputs:
X - sampled sequence, np.array of size (n_samples, n_features)
mix_idx - the component which the sequence was sampled from,
integer.
state_seq - the produced state sequence, np.int of size n_samples.
'''
if Xpref is not None:
pref_len = Xpref.shape[0]
mix, trans = self._compute_mixture_posteriors(Xpref, y, [pref_len])
mix_post = np.exp(mix)
else:
mix_post = self.mixCoef[y, :]
mix_idx = np.random.choice(self.mix_dim, p=mix_post.reshape(-1))
if Xpref is not None:
state_prior = self.mixModels[mix_idx].startprob_
state_post = self.mixModels[mix_idx].predict_proba(Xpref)[-1, :]
self.mixModels[mix_idx].startprob_ = state_post
X, state_seq = self.mixModels[mix_idx].sample(n_samples=n_samples)
if Xpref is not None:
self.mixModels[mix_idx].startprob_ = state_prior
return X, mix_idx, state_seq
def fit(self, X, lengths=None):
X = check_array(X)
self._init(X, lengths=lengths)
self._check()
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, self.verbose)
for iter in range(self.n_iter):
print('iteration: {}'.format(iter))
stats = self._initialize_sufficient_statistics()
curr_logprob = 0
tt = 0
path_list = list()
for i, j in iter_from_X_lengths(X, lengths):
logprob, state_sequence = self.decode(X[i:j],
algorithm="viterbi")
curr_logprob += logprob
epsilon = np.zeros((state_sequence.shape[0] - 1,
self.n_components, self.n_components))
gamma = np.zeros((state_sequence.shape[0], self.n_components))
for t in range(state_sequence.shape[0] - 1):
epsilon[t, state_sequence[t], state_sequence[t + 1]] = 1
for t in range(state_sequence.shape[0]):
for i in range(self.n_components):
if t != (state_sequence.shape[0] - 1):
gamma[t, i] = np.sum(epsilon[t, i])
else:
gamma[t, i] = gamma[t - 1, i]
path_list.append(state_sequence)
self._accumulate_sufficient_statistics(stats, X[i:j], epsilon,
gamma, state_sequence,
None)
tt += 1
print('average loss: {}'.format(curr_logprob / tt))
if not fast_update:
stats['start'] /= tt
stats['trans'] /= tt
self._do_mstep(stats)
if update_dnn:
temp_path = np.zeros((0, 1))
for k, (i, j) in enumerate(iter_from_X_lengths(X,
lengths)):
temp_path = np.vstack(
[temp_path,
np.array(path_list[k]).reshape(-1, 1)])
self.mlp.train(X, temp_path, 20)
acoustic_model = np.zeros(self.n_components)
for i, j in iter_from_X_lengths(X, lengths):
logprob, state_sequence = self.decode(X[i:j],
algorithm="viterbi")
for state in state_sequence:
acoustic_model[state] += 1
self.aucoustic_model = acoustic_model / np.sum(acoustic_model)
self.monitor_.report(curr_logprob)
if self.monitor_.iter == self.monitor_.n_iter or \
(len(self.monitor_.history) == 2 and
abs(self.monitor_.history[1] - self.monitor_.history[0]) < self.monitor_.tol * abs(
self.monitor_.history[1])):
break
print('----------------------------------------------')
return self
def fit(self, X, y, lengths=None, valid_data=None):
'''
Trains SpaMHMM on data X, y, using the EM algorithm.
Inputs:
X - np.array of size (n_samples, n_features).
y - np.int of size n_sequences, whose entries are in the
range [0, n_nodes-1].
lengths - list containing the lengths of each individual sequence
in X, with size n_sequences.
valid_data - tuple (X_valid, y_valid, lengths_valid) containing the
validation data; if validation data is given, the
model with the lowest validation loss is saved in a
pickle file (optional, default:None).
'''
if type(X) == list:
lengths = [x.shape[0] for x in X]
X = np.concatenate(X)
y = np.array(y)
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, False)
if valid_data is not None:
X_valid, y_valid, lengths_valid = valid_data
if type(X_valid) == list:
lengths_valid = [x.shape[0] for x in X_valid]
X_valid = np.concatenate(X_valid)
y_valid = np.array(y_valid)
max_validscore = float('-inf')
validloss_hist = []
if self.graph is not None:
self.reg_ = True
else:
self.reg_ = False
self.init_params(X)
self._check()
for m in range(self.mix_dim):
#self.mixModels[m].means_ = np.array([np.min(X), np.max(X) / 4, np.max(X) / 2, np.max(X)])[:, np.newaxis]
self.mixModels[m].means_ = np.sort(
self.mixModels[m].means_.flatten())[:, np.newaxis] #
#self.mixModels[m].means_ = np.array([4, 9, 17, 25])[:, np.newaxis]
prevscore = float('-inf')
trainloss_hist = []
for it in range(self.n_iter):
t0 = time.time()
stats = self._compute_sufficient_statistics(X, y, lengths)
#similarity = diversified_hmm.get_kernel(self.mixModels[0].transmat_, self.mixModels[1].transmat_) * 1000000000000000
norm0 = math.sqrt(
np.trace(self.mixModels[0].transmat_.dot(
self.mixModels[0].transmat_)))
norm1 = math.sqrt(
np.trace(self.mixModels[1].transmat_.dot(
self.mixModels[1].transmat_)))
similarity = np.trace(self.mixModels[0].transmat_.dot(
self.mixModels[1].transmat_)) / (norm0 * norm1)
from scipy.linalg import det
#similarity = diversified_hmm.get_prior(np.dot(self.mixModels[0].transmat_.T, self.mixModels[1].transmat_))
self.mixModels[
0].similarity = similarity #diversified_hmm.calculate_entropy(self.mixModels[0].transmat_)
self.mixModels[
1].similarity = similarity #diversified_hmm.calculate_entropy(self.mixModels[1].transmat_)
#print('similarity {}'.format(similarity))
self.mixModels[0].iter = it
# if it == 0:
# self.mixModels[0].other_trans = np.array([[.1, 0, .3, .6], [.1, 0, .5, .4], [0, .4, .4, .2], [.2, .2, .2, .4]])
# #self.mixModels[1].other_trans = np.array([[.7, .1, .2, 0], [.1, 0, .2, .7], [.5, .1, .4, 0], [0, .2, .1, .7]])
# else:
self.mixModels[0].other_trans = self.mixModels[1].transmat_
self.mixModels[1].other_trans = self.mixModels[0].transmat_
#self._do_mstep(stats)
if self.reg_:
self._fit_coef(stats)
else:
self.mixCoef = stats['mix_post']
normalize(self.mixCoef, axis=1)
self.mixModels[0].transmat_prior = stats['trans_prior' + str(0)]
self.mixModels[0]._do_mstep(stats['mix_idx' + str(0)])
self.mixModels[1].other_trans = self.mixModels[
0].transmat_ # take the update from this iter
self.mixModels[1].transmat_prior = stats['trans_prior' + str(1)]
self.mixModels[1]._do_mstep(stats['mix_idx' + str(1)])
####
print('trans0 {}'.format(self.mixModels[0].transmat_))
print('trans1 {}'.format(self.mixModels[1].transmat_))
t1 = time.time()
currscore = self.score(X, y, lengths)
trainloss_hist.append(-currscore)
if valid_data is not None:
validscore = self.score(X_valid, y_valid, lengths_valid)
validloss_hist.append(-validscore)
if validscore > max_validscore:
max_validscore = validscore
f = open(self.name + '.pkl', 'wb')
pickle.dump(self, f)
if self.verbose:
if (not self.reg_) and (prevscore > currscore):
print(
'WARNING: loss has increased at iteration {}!'.format(
it))
print('prev loss = {:.5f}, curr loss = {:.5f}'.format(
-prevscore, -currscore))
elif valid_data is not None:
print('it {}: train loss = {:.5f}, valid loss = {:.5f}, '
'{:.3f} sec/it'.format(it + 1, -currscore,
-validscore, t1 - t0))
else:
print('it {}: loss = {:.5f}, {:.3f} sec/it'.format(
it + 1, -currscore, t1 - t0))
ll = np.sum(self.scores_per_seq(X, y, lengths))
print("ll: {}".format(ll))
# ll = 0
# for m in range(self.mix_dim):
# ll += np.max(self.mixModels[m]._compute_log_likelihood(X))
self.monitor_.report(currscore)
# self.monitor_.report(ll)
# print("ll: {}".format(ll))
if self.monitor_.converged:
if self.verbose:
print(
'Loss improved less than {}. Training stopped.'.format(
self.tol))
break
prevscore = currscore
if valid_data:
return trainloss_hist, validloss_hist
else:
return trainloss_hist
class SemiSupervisedGaussianHMM(GaussianHMM):
def __init__(self, n_components=1, covariance_type='diag', min_covar=1e-3, startprob_prior=1.0,
transmat_prior=1.0, means_prior=0, means_weight=0, covars_prior=1e-2, covars_weight=1,
algorithm="viterbi", random_state=None, n_iter=5, tol=1e-2, verbose=False,
params="stmc", init_params="stmc", states_prior=None, fp_state=None):
GaussianHMM.__init__(self, n_components=n_components, covariance_type=covariance_type,
min_covar=min_covar, startprob_prior=startprob_prior, transmat_prior=transmat_prior,
means_prior=means_prior, means_weight=means_weight,
covars_prior=covars_prior, covars_weight=covars_weight,
algorithm=algorithm, random_state=random_state,
n_iter=n_iter, tol=tol, verbose=verbose,
params=params, init_params=init_params)
self.covariance_type = covariance_type
self.min_covar = min_covar
self.means_prior = means_prior
self.means_weight = means_weight
self.covars_prior = covars_prior
self.covars_weight = covars_weight
self.states_prior = states_prior
self.fp_state = fp_state
def fit(self, X, lengths=None):
"""Estimate model parameters.
An initialization step is performed before entering the
EM algorithm. If you want to avoid this step for a subset of
the parameters, pass proper ``init_params`` keyword argument
to estimator's constructor.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Feature matrix of individual samples.
lengths : array-like of integers, shape (n_sequences, )
Lengths of the individual sequences in ``X``. The sum of
these should be ``n_samples``.
Returns
-------
self : object
Returns self.
"""
X = check_array(X)
self._init(X, lengths=lengths)
self._check()
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, self.verbose)
for iter in range(self.n_iter):
stats = self._initialize_sufficient_statistics()
curr_logprob = 0
for i, j in iter_from_X_lengths(X, lengths):
framelogprob = self._compute_log_likelihood(X[i:j])
logprob, fwdlattice = self._do_forward_pass(framelogprob)
curr_logprob += logprob
bwdlattice = self._do_backward_pass(framelogprob)
posteriors = self._compute_posteriors(fwdlattice, bwdlattice)
# fix posteriors
if self.states_prior is not None and self.fp_state is not None:
for k in range(len(self.states_prior)):
if self.states_prior[k] == 0:
# non footprint states
posteriors[k][self.fp_state] = 0.0
posteriors[k] = posteriors[k] / sum(posteriors[k])
elif self.states_prior[k] == 1:
# footprint states
posteriors[k] = 0.0 / sum(posteriors[k])
posteriors[k][self.fp_state] = 1.0
self._accumulate_sufficient_statistics(stats, X[i:j], framelogprob, posteriors, fwdlattice, bwdlattice)
self._do_mstep(stats)
self.monitor_.report(curr_logprob)
if self.monitor_.converged:
break
return self
def fit(self, X, y, lengths=None, valid_data=None):
'''
Trains SpaMHMM on data X, y, using the EM algorithm.
Inputs:
X - np.array of size (n_samples, n_features).
y - np.int of size n_sequences, whose entries are in the
range [0, n_nodes-1].
lengths - list containing the lengths of each individual sequence
in X, with size n_sequences.
valid_data - tuple (X_valid, y_valid, lengths_valid) containing the
validation data; if validation data is given, the
model with the lowest validation loss is saved in a
pickle file (optional, default:None).
'''
if type(X) == list:
lengths = [x.shape[0] for x in X]
X = np.concatenate(X)
y = np.array(y)
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, False)
if valid_data is not None:
X_valid, y_valid, lengths_valid = valid_data
if type(X_valid) == list:
lengths_valid = [x.shape[0] for x in X_valid]
X_valid = np.concatenate(X_valid)
y_valid = np.array(y_valid)
max_validscore = float('-inf')
validloss_hist = []
if self.graph is not None:
self.reg_ = True
else:
self.reg_ = False
self.init_params(X)
self._check()
prevscore = float('-inf')
trainloss_hist = []
for it in range(self.n_iter):
t0 = time.time()
stats = self._compute_sufficient_statistics(X, y, lengths)
self._do_mstep(stats)
print('trans0 {}'.format(self.mixModels[0].transmat_))
print('trans1 {}'.format(self.mixModels[1].transmat_))
t1 = time.time()
currscore = self.score(X, y, lengths)
trainloss_hist.append(-currscore)
if valid_data is not None:
validscore = self.score(X_valid, y_valid, lengths_valid)
validloss_hist.append(-validscore)
if validscore > max_validscore:
max_validscore = validscore
f = open(self.name + '.pkl', 'wb')
pickle.dump(self, f)
if self.verbose:
if (not self.reg_) and (prevscore > currscore):
print(
'WARNING: loss has increased at iteration {}!'.format(
it))
print('prev loss = {:.5f}, curr loss = {:.5f}'.format(
-prevscore, -currscore))
elif valid_data is not None:
print('it {}: train loss = {:.5f}, valid loss = {:.5f}, '
'{:.3f} sec/it'.format(it + 1, -currscore,
-validscore, t1 - t0))
else:
print('it {}: loss = {:.5f}, {:.3f} sec/it'.format(
it + 1, -currscore, t1 - t0))
ll = np.sum(self.scores_per_seq(X, y, lengths))
print("ll: {}".format(ll))
# ll = 0
# for m in range(self.mix_dim):
# ll += np.max(self.mixModels[m]._compute_log_likelihood(X))
self.monitor_.report(currscore)
# self.monitor_.report(ll)
# print("ll: {}".format(ll))
if self.monitor_.converged:
if self.verbose:
print(
'Loss improved less than {}. Training stopped.'.format(
self.tol))
break
prevscore = currscore
if valid_data:
return trainloss_hist, validloss_hist
else:
return trainloss_hist
class hmm_dnn(_BaseHMM):
def __init__(self,
mlp,
aucoustic_model,
observation_count,
n_components=1,
startprob_prior=1.0,
transmat_prior=1.0,
algorithm="viterbi",
random_state=None,
n_iter=10,
tol=1e-2,
verbose=False,
params="stmc",
init_params="stmc"):
_BaseHMM.__init__(self,
n_components,
startprob_prior=startprob_prior,
transmat_prior=transmat_prior,
algorithm=algorithm,
random_state=random_state,
n_iter=n_iter,
tol=tol,
params=params,
verbose=verbose,
init_params=init_params)
self.aucoustic_model = aucoustic_model
self.observation_count = observation_count
self.mlp = mlp
self.mlp.info()
def _compute_log_likelihood(self, X):
prob = self.mlp.log_probablity(X).astype(type(X[0, 0]))
prob = prob - np.log(self.observation_count)
prob = prob - np.log(self.aucoustic_model +
(self.aucoustic_model == 0))
return prob
def _accumulate_sufficient_statistics(self, stats, X, epsilon, gamma, path,
bwdlattice):
stats['nobs'] += 1
if 's' in self.params:
stats['start'] += gamma[0]
if 't' in self.params:
n_samples = X.shape[0]
if n_samples <= 1:
return
a = np.zeros((self.n_components, self.n_components))
for i in range(self.n_components):
for j in range(self.n_components):
a[i, j] = np.sum(epsilon[:, i,
j]) / (np.sum(gamma[:, i]) +
(np.sum(gamma[:, i]) == 0))
stats['trans'] += a
def fit(self, X, lengths=None):
X = check_array(X)
self._init(X, lengths=lengths)
self._check()
self.monitor_ = ConvergenceMonitor(self.tol, self.n_iter, self.verbose)
for iter in range(self.n_iter):
print('iteration: {}'.format(iter))
stats = self._initialize_sufficient_statistics()
curr_logprob = 0
tt = 0
path_list = list()
for i, j in iter_from_X_lengths(X, lengths):
logprob, state_sequence = self.decode(X[i:j],
algorithm="viterbi")
curr_logprob += logprob
epsilon = np.zeros((state_sequence.shape[0] - 1,
self.n_components, self.n_components))
gamma = np.zeros((state_sequence.shape[0], self.n_components))
for t in range(state_sequence.shape[0] - 1):
epsilon[t, state_sequence[t], state_sequence[t + 1]] = 1
for t in range(state_sequence.shape[0]):
for i in range(self.n_components):
if t != (state_sequence.shape[0] - 1):
gamma[t, i] = np.sum(epsilon[t, i])
else:
gamma[t, i] = gamma[t - 1, i]
path_list.append(state_sequence)
self._accumulate_sufficient_statistics(stats, X[i:j], epsilon,
gamma, state_sequence,
None)
tt += 1
print('average loss: {}'.format(curr_logprob / tt))
if not fast_update:
stats['start'] /= tt
stats['trans'] /= tt
self._do_mstep(stats)
if update_dnn:
temp_path = np.zeros((0, 1))
for k, (i, j) in enumerate(iter_from_X_lengths(X,
lengths)):
temp_path = np.vstack(
[temp_path,
np.array(path_list[k]).reshape(-1, 1)])
self.mlp.train(X, temp_path, 20)
acoustic_model = np.zeros(self.n_components)
for i, j in iter_from_X_lengths(X, lengths):
logprob, state_sequence = self.decode(X[i:j],
algorithm="viterbi")
for state in state_sequence:
acoustic_model[state] += 1
self.aucoustic_model = acoustic_model / np.sum(acoustic_model)
self.monitor_.report(curr_logprob)
if self.monitor_.iter == self.monitor_.n_iter or \
(len(self.monitor_.history) == 2 and
abs(self.monitor_.history[1] - self.monitor_.history[0]) < self.monitor_.tol * abs(
self.monitor_.history[1])):
break
print('----------------------------------------------')
return self
def _do_mstep(self, stats):
if 's' in self.params:
startprob_ = stats['start']
self.startprob_ = np.where(self.startprob_ == 0.0, self.startprob_,
startprob_)
normalize(self.startprob_)
if 't' in self.params:
transmat_ = stats['trans']
self.transmat_ = np.where(self.transmat_ == 0.0, self.transmat_,
transmat_)
normalize(self.transmat_, axis=1)
for i, row in enumerate(self.transmat_):
if not np.any(row):
self.transmat_[i][i] = 1
