def test_2state_2obs_Pgiven(self):
obs = np.array([0, 0, 1, 1, 0])
C = msmest.count_matrix(obs, 1).toarray()
Aref = np.array([[1.0]])
for rev in [True, False]: # reversibiliy doesn't matter in this example
P = msmest.transition_matrix(C, reversible=rev)
p0, P0, B0 = init_discrete_hmm_spectral(C, 1, reversible=rev, P=P)
assert(np.allclose(P0, Aref))
# output must be 1 x 2, and no zeros
assert(np.array_equal(B0.shape, np.array([1, 2])))
assert(np.all(B0 > 0.0))
def init_discrete_hmm(observations, nstates, lag=1, reversible=True, stationary=True, regularize=True,
method='connect-spectral', separate=None):
"""Use a heuristic scheme to generate an initial model.
Parameters
----------
observations : list of ndarray((T_i))
list of arrays of length T_i with observation data
nstates : int
The number of states.
lag : int
Lag time at which the observations should be counted.
reversible : bool
Estimate reversible HMM transition matrix.
stationary : bool
p0 is the stationary distribution of P. Currently only reversible=True is implemented
regularize : bool
Regularize HMM probabilities to avoid 0's.
method : str
* 'lcs-spectral' : Does spectral clustering on the largest connected set
of observed states.
* 'connect-spectral' : Uses a weak regularization to connect the weakly
connected sets and then initializes HMM using spectral clustering on
the nonempty set.
* 'spectral' : Uses spectral clustering on the nonempty subsets. Separated
observed states will end up in separate hidden states. This option is
only recommended for small observation spaces. Use connect-spectral for
large observation spaces.
separate : None or iterable of int
Force the given set of observed states to stay in a separate hidden state.
The remaining nstates-1 states will be assigned by a metastable decomposition.
Examples
--------
Generate initial model for a discrete output model.
>>> import bhmm
>>> [model, observations, states] = bhmm.testsystems.generate_synthetic_observations(output='discrete')
>>> initial_model = init_discrete_hmm(observations, model.nstates)
"""
import msmtools.estimation as msmest
from bhmm.init.discrete import init_discrete_hmm_spectral
C = msmest.count_matrix(observations, lag).toarray()
# regularization
if regularize:
eps_A = None
eps_B = None
else:
eps_A = 0
eps_B = 0
if not stationary:
raise NotImplementedError('Discrete-HMM initialization with stationary=False is not yet implemented.')
if method=='lcs-spectral':
lcs = msmest.largest_connected_set(C)
p0, P, B = init_discrete_hmm_spectral(C, nstates, reversible=reversible, stationary=stationary,
active_set=lcs, separate=separate, eps_A=eps_A, eps_B=eps_B)
elif method=='connect-spectral':
# make sure we're strongly connected
C += msmest.prior_neighbor(C, 0.001)
nonempty = _np.where(C.sum(axis=0) + C.sum(axis=1) > 0)[0]
C[nonempty, nonempty] = _np.maximum(C[nonempty, nonempty], 0.001)
p0, P, B = init_discrete_hmm_spectral(C, nstates, reversible=reversible, stationary=stationary,
active_set=nonempty, separate=separate, eps_A=eps_A, eps_B=eps_B)
elif method=='spectral':
p0, P, B = init_discrete_hmm_spectral(C, nstates, reversible=reversible, stationary=stationary,
active_set=None, separate=separate, eps_A=eps_A, eps_B=eps_B)
else:
raise NotImplementedError('Unknown discrete-HMM initialization method ' + str(method))
hmm0 = discrete_hmm(p0, P, B)
hmm0._lag = lag
return hmm0
def _estimate(self, dtrajs):
import bhmm
# ensure right format
dtrajs = _types.ensure_dtraj_list(dtrajs)
# CHECK LAG
trajlengths = [_np.size(dtraj) for dtraj in dtrajs]
if self.lag >= _np.max(trajlengths):
raise ValueError('Illegal lag time ' + str(self.lag) + ' exceeds longest trajectory length')
if self.lag > _np.mean(trajlengths):
self.logger.warning('Lag time ' + str(self.lag) + ' is on the order of mean trajectory length '
+ str(_np.mean(trajlengths)) + '. It is recommended to fit four lag times in each '
+ 'trajectory. HMM might be inaccurate.')
# EVALUATE STRIDE
if self.stride == 'effective':
# by default use lag as stride (=lag sampling), because we currently have no better theory for deciding
# how many uncorrelated counts we can make
self.stride = self.lag
# get a quick estimate from the spectral radius of the nonreversible
from pyemma.msm import estimate_markov_model
msm_nr = estimate_markov_model(dtrajs, lag=self.lag, reversible=False, sparse=False,
connectivity='largest', dt_traj=self.timestep_traj)
# if we have more than nstates timescales in our MSM, we use the next (neglected) timescale as an
# estimate of the decorrelation time
if msm_nr.nstates > self.nstates:
corrtime = max(1, msm_nr.timescales()[self.nstates-1])
# use the smaller of these two pessimistic estimates
self.stride = int(min(self.lag, 2*corrtime))
# LAG AND STRIDE DATA
dtrajs_lagged_strided = bhmm.lag_observations(dtrajs, self.lag, stride=self.stride)
# OBSERVATION SET
if self.observe_nonempty:
observe_subset = 'nonempty'
else:
observe_subset = None
# INIT HMM
from bhmm import init_discrete_hmm
from pyemma.msm.estimators import MaximumLikelihoodMSM
if self.msm_init=='largest-strong':
hmm_init = init_discrete_hmm(dtrajs_lagged_strided, self.nstates, lag=1,
reversible=self.reversible, stationary=True, regularize=True,
method='lcs-spectral', separate=self.separate)
elif self.msm_init=='all':
hmm_init = init_discrete_hmm(dtrajs_lagged_strided, self.nstates, lag=1,
reversible=self.reversible, stationary=True, regularize=True,
method='spectral', separate=self.separate)
elif issubclass(self.msm_init.__class__, MaximumLikelihoodMSM): # initial MSM given.
from bhmm.init.discrete import init_discrete_hmm_spectral
p0, P0, pobs0 = init_discrete_hmm_spectral(self.msm_init.count_matrix_full, self.nstates,
reversible=self.reversible, stationary=True,
active_set=self.msm_init.active_set,
P=self.msm_init.transition_matrix, separate=self.separate)
hmm_init = bhmm.discrete_hmm(p0, P0, pobs0)
observe_subset = self.msm_init.active_set # override observe_subset.
else:
raise ValueError('Unknown MSM initialization option: ' + str(self.msm_init))
# ---------------------------------------------------------------------------------------
# Estimate discrete HMM
# ---------------------------------------------------------------------------------------
# run EM
from bhmm.estimators.maximum_likelihood import MaximumLikelihoodEstimator as _MaximumLikelihoodEstimator
hmm_est = _MaximumLikelihoodEstimator(dtrajs_lagged_strided, self.nstates, initial_model=hmm_init,
output='discrete', reversible=self.reversible, stationary=self.stationary,
accuracy=self.accuracy, maxit=self.maxit)
# run
hmm_est.fit()
# package in discrete HMM
self.hmm = bhmm.DiscreteHMM(hmm_est.hmm)
# get model parameters
self.initial_distribution = self.hmm.initial_distribution
transition_matrix = self.hmm.transition_matrix
observation_probabilities = self.hmm.output_probabilities
# get estimation parameters
self.likelihoods = hmm_est.likelihoods # Likelihood history
self.likelihood = self.likelihoods[-1]
self.hidden_state_probabilities = hmm_est.hidden_state_probabilities # gamma variables
self.hidden_state_trajectories = hmm_est.hmm.hidden_state_trajectories # Viterbi path
self.count_matrix = hmm_est.count_matrix # hidden count matrix
self.initial_count = hmm_est.initial_count # hidden init count
self._active_set = _np.arange(self.nstates)
# TODO: it can happen that we loose states due to striding. Should we lift the output probabilities afterwards?
# parametrize self
self._dtrajs_full = dtrajs
self._dtrajs_lagged = dtrajs_lagged_strided
self._nstates_obs_full = msmest.number_of_states(dtrajs)
self._nstates_obs = msmest.number_of_states(dtrajs_lagged_strided)
self._observable_set = _np.arange(self._nstates_obs)
self._dtrajs_obs = dtrajs
self.set_model_params(P=transition_matrix, pobs=observation_probabilities,
reversible=self.reversible, dt_model=self.timestep_traj.get_scaled(self.lag))
# TODO: perhaps remove connectivity and just rely on .submodel()?
# deal with connectivity
states_subset = None
if self.connectivity == 'largest':
states_subset = 'largest-strong'
elif self.connectivity == 'populous':
states_subset = 'populous-strong'
# return submodel (will return self if all None)
return self.submodel(states=states_subset, obs=observe_subset, mincount_connectivity=self.mincount_connectivity)
def init_discrete_hmm(observations,
nstates,
lag=1,
reversible=True,
stationary=True,
regularize=True,
method='connect-spectral',
separate=None):
"""Use a heuristic scheme to generate an initial model.
Parameters
----------
observations : list of ndarray((T_i))
list of arrays of length T_i with observation data
nstates : int
The number of states.
lag : int
Lag time at which the observations should be counted.
reversible : bool
Estimate reversible HMM transition matrix.
stationary : bool
p0 is the stationary distribution of P. Currently only reversible=True is implemented
regularize : bool
Regularize HMM probabilities to avoid 0's.
method : str
* 'lcs-spectral' : Does spectral clustering on the largest connected set
of observed states.
* 'connect-spectral' : Uses a weak regularization to connect the weakly
connected sets and then initializes HMM using spectral clustering on
the nonempty set.
* 'spectral' : Uses spectral clustering on the nonempty subsets. Separated
observed states will end up in separate hidden states. This option is
only recommended for small observation spaces. Use connect-spectral for
large observation spaces.
separate : None or iterable of int
Force the given set of observed states to stay in a separate hidden state.
The remaining nstates-1 states will be assigned by a metastable decomposition.
Examples
--------
Generate initial model for a discrete output model.
>>> import bhmm
>>> [model, observations, states] = bhmm.testsystems.generate_synthetic_observations(output='discrete')
>>> initial_model = init_discrete_hmm(observations, model.nstates)
"""
import msmtools.estimation as msmest
from bhmm.init.discrete import init_discrete_hmm_spectral
C = msmest.count_matrix(observations, lag).toarray()
# regularization
if regularize:
eps_A = None
eps_B = None
else:
eps_A = 0
eps_B = 0
if not stationary:
raise NotImplementedError(
'Discrete-HMM initialization with stationary=False is not yet implemented.'
)
if method == 'lcs-spectral':
lcs = msmest.largest_connected_set(C)
p0, P, B = init_discrete_hmm_spectral(C,
nstates,
reversible=reversible,
stationary=stationary,
active_set=lcs,
separate=separate,
eps_A=eps_A,
eps_B=eps_B)
elif method == 'connect-spectral':
# make sure we're strongly connected
C += msmest.prior_neighbor(C, 0.001)
nonempty = _np.where(C.sum(axis=0) + C.sum(axis=1) > 0)[0]
C[nonempty, nonempty] = _np.maximum(C[nonempty, nonempty], 0.001)
p0, P, B = init_discrete_hmm_spectral(C,
nstates,
reversible=reversible,
stationary=stationary,
active_set=nonempty,
separate=separate,
eps_A=eps_A,
eps_B=eps_B)
elif method == 'spectral':
p0, P, B = init_discrete_hmm_spectral(C,
nstates,
reversible=reversible,
stationary=stationary,
active_set=None,
separate=separate,
eps_A=eps_A,
eps_B=eps_B)
else:
raise NotImplementedError(
'Unknown discrete-HMM initialization method ' + str(method))
hmm0 = discrete_hmm(p0, P, B)
hmm0._lag = lag
return hmm0
