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 _estimate(self, dtrajs):
"""
Parameters
----------
Return
------
hmsm : :class:`EstimatedHMSM <pyemma.msm.estimators.hmsm_estimated.EstimatedHMSM>`
Estimated Hidden Markov state model
"""
# ensure right format
dtrajs = _types.ensure_dtraj_list(dtrajs)
# if no initial MSM is given, estimate it now
if self.msm_init is None:
# estimate with sparse=False, because we need to do PCCA which is currently not implemented for sparse
# estimate with store_data=True, because we need an EstimatedMSM
msm_estimator = _MSMEstimator(lag=self.lag, reversible=self.reversible, sparse=False,
connectivity=self.connectivity, dt_traj=self.timestep_traj)
msm_init = msm_estimator.estimate(dtrajs)
else:
assert isinstance(self.msm_init, _EstimatedMSM), 'msm_init must be of type EstimatedMSM'
msm_init = self.msm_init
self.reversible = msm_init.is_reversible
# print 'Connected set: ', msm_init.active_set
# generate lagged observations
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
# 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_init.nstates > self.nstates:
corrtime = int(max(1, msm_init.timescales()[self.nstates-1]))
# use the smaller of these two pessimistic estimates
self.stride = min(self.stride, 2*corrtime)
# TODO: Here we always use the full observation state space for the estimation.
dtrajs_lagged = _lag_observations(dtrajs, self.lag, stride=self.stride)
# check input
assert _types.is_int(self.nstates) and self.nstates > 1 and self.nstates <= msm_init.nstates, \
'nstates must be an int in [2,msmobj.nstates]'
# if hmm.nstates = msm.nstates there is no problem. Otherwise, check spectral gap
if msm_init.nstates > self.nstates:
timescale_ratios = msm_init.timescales()[:-1] / msm_init.timescales()[1:]
if timescale_ratios[self.nstates-2] < 2.0:
self.logger.warn('Requested coarse-grained model with ' + str(self.nstates) + ' metastable states at ' +
'lag=' + str(self.lag) + '.' + 'The ratio of relaxation timescales between ' +
str(self.nstates) + ' and ' + str(self.nstates+1) + ' states is only ' +
str(timescale_ratios[self.nstates-2]) + ' while we recommend at least 2. ' +
' It is possible that the resulting HMM is inaccurate. Handle with caution.')
# set things from MSM
# TODO: dtrajs_obs is set here, but not used in estimation. Estimation is alwas done with
# TODO: respect to full observation (see above). This is confusing. Define how we want to do this in gen.
# TODO: observable set is also not used, it is just saved.
nstates_obs_full = msm_init.nstates_full
if self.observe_active:
nstates_obs = msm_init.nstates
observable_set = msm_init.active_set
dtrajs_obs = msm_init.discrete_trajectories_active
else:
nstates_obs = msm_init.nstates_full
observable_set = np.arange(nstates_obs_full)
dtrajs_obs = msm_init.discrete_trajectories_full
# TODO: this is redundant with BHMM code because that code is currently not easily accessible and
# TODO: we don't want to re-estimate. Should be reengineered in bhmm.
# ---------------------------------------------------------------------------------------
# PCCA-based coarse-graining
# ---------------------------------------------------------------------------------------
# pcca- to number of metastable states
pcca = msm_init.pcca(self.nstates)
# HMM output matrix
eps = 0.01 * (1.0/nstates_obs_full) # default output probability, in order to avoid zero columns
# Use PCCA distributions, but at least eps to avoid 100% assignment to any state (breaks convergence)
B_conn = np.maximum(msm_init.metastable_distributions, eps)
# full state space output matrix
B = eps * np.ones((self.nstates, nstates_obs_full), dtype=np.float64)
# expand B_conn to full state space
# TODO: here we always select the active set, no matter if observe_active=True or False.
B[:, msm_init.active_set] = B_conn[:, :]
# TODO: at this point we will have zero observation probabilities for states that are not in the active
# TODO: set. If these occur in the trajectory, that will mean zero columns in the output probabilities
# TODO: and crash of forward-backward and sampling algorithms.
# renormalize B to make it row-stochastic
B /= B.sum(axis=1)[:, None]
# coarse-grained transition matrix
P_coarse = pcca.coarse_grained_transition_matrix
# take care of unphysical values. First symmetrize
X = np.dot(np.diag(pcca.coarse_grained_stationary_probability), P_coarse)
X = 0.5*(X + X.T)
# if there are values < 0, set to eps
X = np.maximum(X, eps)
# turn into coarse-grained transition matrix
A = X / X.sum(axis=1)[:, None]
# ---------------------------------------------------------------------------------------
# Estimate discrete HMM
# ---------------------------------------------------------------------------------------
# lazy import bhmm here in order to avoid dependency loops
import bhmm
# initialize discrete HMM
hmm_init = bhmm.discrete_hmm(A, B, stationary=True, reversible=self.reversible)
# run EM
hmm = bhmm.estimate_hmm(dtrajs_lagged, self.nstates, lag=1, initial_model=hmm_init,
accuracy=self.accuracy, maxit=self.maxit)
self.hmm = bhmm.DiscreteHMM(hmm)
# find observable set
transition_matrix = self.hmm.transition_matrix
observation_probabilities = self.hmm.output_probabilities
# TODO: Cutting down... OK, this can be done
if self.observe_active: # cut down observation probabilities to active set
observation_probabilities = observation_probabilities[:, msm_init.active_set]
observation_probabilities /= observation_probabilities.sum(axis=1)[:,None] # renormalize
# parametrize self
self._dtrajs_full = dtrajs
self._dtrajs_lagged = dtrajs_lagged
self._observable_set = observable_set
self._dtrajs_obs = dtrajs_obs
self.set_model_params(P=transition_matrix, pobs=observation_probabilities,
reversible=self.reversible, dt_model=self.timestep_traj.get_scaled(self.lag))
return self
