class MaximumLikelihoodHMSM(_Estimator, _HMSM):
r"""Maximum likelihood estimator for a Hidden MSM given a MSM"""
def __init__(self, nstates=2, lag=1, stride=1, msm_init='largest-strong', reversible=True, stationary=False,
connectivity=None, mincount_connectivity='1/n', observe_nonempty=True, separate=None,
dt_traj='1 step', accuracy=1e-3, maxit=1000):
r"""Maximum likelihood estimator for a Hidden MSM given a MSM
Parameters
----------
nstates : int, optional, default=2
number of hidden states
lag : int, optional, default=1
lagtime to estimate the HMSM at
stride : str or int, default=1
stride between two lagged trajectories extracted from the input
trajectories. Given trajectory s[t], stride and lag will result
in trajectories
s[0], s[lag], s[2 lag], ...
s[stride], s[stride + lag], s[stride + 2 lag], ...
Setting stride = 1 will result in using all data (useful for maximum
likelihood estimator), while a Bayesian estimator requires a longer
stride in order to have statistically uncorrelated trajectories.
Setting stride = 'effective' uses the largest neglected timescale as
an estimate for the correlation time and sets the stride accordingly
msm_init : str or :class:`MSM <pyemma.msm.MSM>`
MSM object to initialize the estimation, or one of following keywords:
* 'largest-strong' or None (default) : Estimate MSM on the largest
strongly connected set and use spectral clustering to generate an
initial HMM
* 'all' : Estimate MSM(s) on the full state space to initialize the
HMM. This estimate maybe weakly connected or disconnected.
reversible : bool, optional, default = True
If true compute reversible MSM, else non-reversible MSM
stationary : bool, optional, default=False
If True, the initial distribution of hidden states is self-consistently computed as the stationary
distribution of the transition matrix. If False, it will be estimated from the starting states.
Only set this to true if you're sure that the observation trajectories are initiated from a global
equilibrium distribution.
connectivity : str, optional, default = None
Defines if the resulting HMM will be defined on all hidden states or on
a connected subset. Connectivity is defined by counting only
transitions with at least mincount_connectivity counts.
If a subset of states is used, all estimated quantities (transition
matrix, stationary distribution, etc) are only defined on this subset
and are correspondingly smaller than nstates.
Following modes are available:
* None or 'all' : The active set is the full set of states.
Estimation is done on all weakly connected subsets separately. The
resulting transition matrix may be disconnected.
* 'largest' : The active set is the largest reversibly connected set.
* 'populous' : The active set is the reversibly connected set with most counts.
mincount_connectivity : float or '1/n'
minimum number of counts to consider a connection between two states.
Counts lower than that will count zero in the connectivity check and
may thus separate the resulting transition matrix. The default
evaluates to 1/nstates.
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.
observe_nonempty : bool
If True, will restricted the observed states to the states that have
at least one observation in the lagged input trajectories.
If an initial MSM is given, this option is ignored and the observed
subset is always identical to the active set of that MSM.
dt_traj : str, optional, default='1 step'
Description of the physical time corresponding to the trajectory time
step. May be used by analysis algorithms such as plotting tools to
pretty-print the axes. By default '1 step', i.e. there is no physical
time unit. Specify by a number, whitespace and unit. Permitted units
are (* is an arbitrary string):
| 'fs', 'femtosecond*'
| 'ps', 'picosecond*'
| 'ns', 'nanosecond*'
| 'us', 'microsecond*'
| 'ms', 'millisecond*'
| 's', 'second*'
accuracy : float, optional, default = 1e-3
convergence threshold for EM iteration. When two the likelihood does
not increase by more than accuracy, the iteration is stopped
successfully.
maxit : int, optional, default = 1000
stopping criterion for EM iteration. When so many iterations are
performed without reaching the requested accuracy, the iteration is
stopped without convergence (a warning is given)
"""
self.nstates = nstates
self.lag = lag
self.stride = stride
self.msm_init = msm_init
self.reversible = reversible
self.stationary = stationary
self.connectivity = connectivity
if mincount_connectivity == '1/n':
mincount_connectivity = 1.0/float(nstates)
self.mincount_connectivity = mincount_connectivity
self.separate = separate
self.observe_nonempty = observe_nonempty
self.dt_traj = dt_traj
self.timestep_traj = TimeUnit(dt_traj)
self.accuracy = accuracy
self.maxit = maxit
#TODO: store_data is mentioned but not implemented or used!
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)
@property
def lagtime(self):
""" The lag time in steps """
return self.lag
@property
def nstates_obs(self):
r""" Number of states in discrete trajectories """
return self._nstates_obs
@property
def active_set(self):
"""
The active set of hidden states on which all hidden state computations are done
"""
if hasattr(self, '_active_set'):
return self._active_set
else:
return _np.arange(self.nstates) # all hidden states are active.
@property
def observable_set(self):
"""
The active set of states on which all computations and estimations will be done
"""
return self._observable_set
@property
@alias('dtrajs_full')
def discrete_trajectories_full(self):
"""
A list of integer arrays with the original trajectories.
"""
return self._dtrajs_full
@property
@alias('dtrajs_lagged')
def discrete_trajectories_lagged(self):
"""
Transformed original trajectories that are used as an input into the HMM estimation
"""
return self._dtrajs_lagged
@property
@alias('dtrajs_obs')
def discrete_trajectories_obs(self):
"""
A list of integer arrays with the discrete trajectories mapped to the observation mode used.
When using observe_active = True, the indexes will be given on the MSM active set. Frames that are not in the
observation set will be -1. When observe_active = False, this attribute is identical to
discrete_trajectories_full
"""
return self._dtrajs_obs
################################################################################
# Submodel functions using estimation information (counts)
################################################################################
def submodel(self, states=None, obs=None, mincount_connectivity='1/n'):
"""Returns a HMM with restricted state space
Parameters
----------
states : None, str or int-array
Hidden states to restrict the model to. In addition to specifying
the subset, possible options are:
* None : all states - don't restrict
* 'populous-strong' : strongly connected subset with maximum counts
* 'populous-weak' : weakly connected subset with maximum counts
* 'largest-strong' : strongly connected subset with maximum size
* 'largest-weak' : weakly connected subset with maximum size
obs : None, str or int-array
Observed states to restrict the model to. In addition to specifying
an array with the state labels to be observed, possible options are:
* None : all states - don't restrict
* 'nonempty' : all states with at least one observation in the estimator
mincount_connectivity : float or '1/n'
minimum number of counts to consider a connection between two states.
Counts lower than that will count zero in the connectivity check and
may thus separate the resulting transition matrix. Default value:
1/nstates.
Returns
-------
hmm : HMM
The restricted HMM.
"""
if states is None and obs is None and mincount_connectivity == 0:
return self
if states is None:
states = _np.arange(self.nstates)
if obs is None:
obs = _np.arange(self.nstates_obs)
if str(mincount_connectivity) == '1/n':
mincount_connectivity = 1.0/float(self.nstates)
# handle new connectivity
from bhmm.estimators import _tmatrix_disconnected
S = _tmatrix_disconnected.connected_sets(self.count_matrix,
mincount_connectivity=mincount_connectivity,
strong=True)
if len(S) > 1:
# keep only non-negligible transitions
C = _np.zeros(self.count_matrix.shape)
large = _np.where(self.count_matrix >= mincount_connectivity)
C[large] = self.count_matrix[large]
for s in S: # keep all (also small) transition counts within strongly connected subsets
C[_np.ix_(s, s)] = self.count_matrix[_np.ix_(s, s)]
# re-estimate transition matrix with disc.
P = _tmatrix_disconnected.estimate_P(C, reversible=self.reversible, mincount_connectivity=0)
pi = _tmatrix_disconnected.stationary_distribution(P, C)
else:
C = self.count_matrix
P = self.transition_matrix
pi = self.stationary_distribution
# determine substates
if isinstance(states, str):
from bhmm.estimators import _tmatrix_disconnected
strong = 'strong' in states
largest = 'largest' in states
S = _tmatrix_disconnected.connected_sets(self.count_matrix, mincount_connectivity=mincount_connectivity,
strong=strong)
if largest:
score = [len(s) for s in S]
else:
score = [self.count_matrix[_np.ix_(s, s)].sum() for s in S]
states = _np.array(S[_np.argmax(score)])
if states is not None: # sub-transition matrix
self._active_set = states
C = C[_np.ix_(states, states)].copy()
P = P[_np.ix_(states, states)].copy()
P /= P.sum(axis=1)[:, None]
pi = _tmatrix_disconnected.stationary_distribution(P, C)
self.initial_count = self.initial_count[states]
self.initial_distribution = self.initial_distribution[states] / self.initial_distribution[states].sum()
# determine observed states
if str(obs) == 'nonempty':
import msmtools.estimation as msmest
obs = _np.where(msmest.count_states(self.discrete_trajectories_lagged) > 0)[0]
if obs is not None:
# set observable set
self._observable_set = obs
self._nstates_obs = obs.size
# full2active mapping
_full2obs = -1 * _np.ones(self._nstates_obs_full, dtype=int)
_full2obs[obs] = _np.arange(len(obs), dtype=int)
# observable trajectories
self._dtrajs_obs = []
for dtraj in self.discrete_trajectories_full:
self._dtrajs_obs.append(_full2obs[dtraj])
# observation matrix
B = self.observation_probabilities[_np.ix_(states, obs)].copy()
B /= B.sum(axis=1)[:, None]
else:
B = self.observation_probabilities
# set quantities back.
self.update_model_params(P=P, pobs=B, pi=pi)
self.count_matrix_EM = self.count_matrix[_np.ix_(states, states)] # unchanged count matrix
self.count_matrix = C # count matrix consistent with P
return self
def submodel_largest(self, strong=True, mincount_connectivity='1/n'):
""" Returns the largest connected sub-HMM (convenience function)
Returns
-------
hmm : HMM
The restricted HMM.
"""
if strong:
return self.submodel(states='largest-strong', mincount_connectivity=mincount_connectivity)
else:
return self.submodel(states='largest-weak', mincount_connectivity=mincount_connectivity)
def submodel_populous(self, strong=True, mincount_connectivity='1/n'):
""" Returns the most populous connected sub-HMM (convenience function)
Returns
-------
hmm : HMM
The restricted HMM.
"""
if strong:
return self.submodel(states='populous-strong', mincount_connectivity=mincount_connectivity)
else:
return self.submodel(states='populous-weak', mincount_connectivity=mincount_connectivity)
def submodel_disconnect(self, mincount_connectivity='1/n'):
"""Disconnects sets of hidden states that are barely connected
Runs a connectivity check excluding all transition counts below
mincount_connectivity. The transition matrix and stationary distribution
will be re-estimated. Note that the resulting transition matrix
may have both strongly and weakly connected subsets.
Parameters
----------
mincount_connectivity : float or '1/n'
minimum number of counts to consider a connection between two states.
Counts lower than that will count zero in the connectivity check and
may thus separate the resulting transition matrix. The default
evaluates to 1/nstates.
Returns
-------
hmm : HMM
The restricted HMM.
"""
return self.submodel(mincount_connectivity=mincount_connectivity)
def trajectory_weights(self):
r"""Uses the HMSM to assign a probability weight to each trajectory frame.
This is a powerful function for the calculation of arbitrary observables in the trajectories one has
started the analysis with. The stationary probability of the MSM will be used to reweigh all states.
Returns a list of weight arrays, one for each trajectory, and with a number of elements equal to
trajectory frames. Given :math:`N` trajectories of lengths :math:`T_1` to :math:`T_N`, this function
returns corresponding weights:
.. math::
(w_{1,1}, ..., w_{1,T_1}), (w_{N,1}, ..., w_{N,T_N})
that are normalized to one:
.. math::
\sum_{i=1}^N \sum_{t=1}^{T_i} w_{i,t} = 1
Suppose you are interested in computing the expectation value of a function :math:`a(x)`, where :math:`x`
are your input configurations. Use this function to compute the weights of all input configurations and
obtain the estimated expectation by:
.. math::
\langle a \rangle = \sum_{i=1}^N \sum_{t=1}^{T_i} w_{i,t} a(x_{i,t})
Or if you are interested in computing the time-lagged correlation between functions :math:`a(x)` and
:math:`b(x)` you could do:
.. math::
\langle a(t) b(t+\tau) \rangle_t = \sum_{i=1}^N \sum_{t=1}^{T_i} w_{i,t} a(x_{i,t}) a(x_{i,t+\tau})
Returns
-------
The normalized trajectory weights. Given :math:`N` trajectories of lengths :math:`T_1` to :math:`T_N`,
returns the corresponding weights:
.. math::
(w_{1,1}, ..., w_{1,T_1}), (w_{N,1}, ..., w_{N,T_N})
"""
# compute stationary distribution, expanded to full set
statdist = self.stationary_distribution_obs
statdist = _np.append(statdist, [-1]) # add a zero weight at index -1, to deal with unobserved states
# histogram observed states
import msmtools.dtraj as msmtraj
hist = 1.0 * msmtraj.count_states(self.discrete_trajectories_obs, ignore_negative=True)
# simply read off stationary distribution and accumulate total weight
W = []
wtot = 0.0
for dtraj in self.discrete_trajectories_obs:
w = statdist[dtraj] / hist[dtraj]
W.append(w)
wtot += _np.sum(w)
# normalize
for w in W:
w /= wtot
# done
return W
################################################################################
# Generation of trajectories and samples
################################################################################
@property
def observable_state_indexes(self):
"""
Ensures that the observable states are indexed and returns the indices
"""
try: # if we have this attribute, return it
return self._observable_state_indexes
except AttributeError: # didn't exist? then create it.
import pyemma.util.discrete_trajectories as dt
self._observable_state_indexes = dt.index_states(self.discrete_trajectories_obs)
return self._observable_state_indexes
# TODO: generate_traj. How should that be defined? Probably indexes of observable states, but should we specify
# hidden or observable states as start and stop states?
# TODO: sample_by_state. How should that be defined?
def sample_by_observation_probabilities(self, nsample):
r"""Generates samples according to given probability distributions
Parameters
----------
distributions : list or array of ndarray ( (n) )
m distributions over states. Each distribution must be of length n and must sum up to 1.0
nsample : int
Number of samples per distribution. If replace = False, the number of returned samples per state could be
smaller if less than nsample indexes are available for a state.
Returns
-------
indexes : length m list of ndarray( (nsample, 2) )
List of the sampled indices by distribution.
Each element is an index array with a number of rows equal to nsample, with rows consisting of a
tuple (i, t), where i is the index of the trajectory and t is the time index within the trajectory.
"""
import pyemma.util.discrete_trajectories as dt
return dt.sample_indexes_by_distribution(self.observable_state_indexes, self.observation_probabilities, nsample)
################################################################################
# Model Validation
################################################################################
def cktest(self, mlags=10, conf=0.95, err_est=False, show_progress=True):
""" Conducts a Chapman-Kolmogorow test.
Parameters
----------
mlags : int or int-array, default=10
multiples of lag times for testing the Model, e.g. range(10).
A single int will trigger a range, i.e. mlags=10 maps to
mlags=range(10). The setting None will choose mlags automatically
according to the longest available trajectory
conf : float, optional, default = 0.95
confidence interval
err_est : bool, default=False
compute errors also for all estimations (computationally expensive)
If False, only the prediction will get error bars, which is often
sufficient to validate a model.
show_progress : bool, default=True
Show progressbars for calculation?
Returns
-------
cktest : :class:`ChapmanKolmogorovValidator <pyemma.msm.ChapmanKolmogorovValidator>`
References
----------
This is an adaption of the Chapman-Kolmogorov Test described in detail
in [1]_ to Hidden MSMs as described in [2]_.
.. [1] Prinz, J H, H Wu, M Sarich, B Keller, M Senne, M Held, J D
Chodera, C Schuette and F Noe. 2011. Markov models of
molecular kinetics: Generation and validation. J Chem Phys
134: 174105
.. [2] F. Noe, H. Wu, J.-H. Prinz and N. Plattner: Projected and hidden
Markov models for calculating kinetics and metastable states of complex
molecules. J. Chem. Phys. 139, 184114 (2013)
"""
from pyemma.msm.estimators import ChapmanKolmogorovValidator
ck = ChapmanKolmogorovValidator(self, self, _np.eye(self.nstates),
mlags=mlags, conf=conf, err_est=err_est,
show_progress=show_progress)
ck.estimate(self._dtrajs_full)
return ck
class MaximumLikelihoodHMSM(_Estimator, _EstimatedHMSM):
r"""Maximum likelihood estimator for a Hidden MSM given a MSM"""
def __init__(self, nstates=2, lag=1, stride=1, msm_init=None, reversible=True, connectivity='largest',
observe_active=True, dt_traj='1 step', accuracy=1e-3, maxit=1000):
r"""Maximum likelihood estimator for a Hidden MSM given a MSM
Parameters
----------
nstates : int, optional, default=2
number of hidden states
lag : int, optional, default=1
lagtime to estimate the HMSM at
stride : str or int, default=1
stride between two lagged trajectories extracted from the input
trajectories. Given trajectory s[t], stride and lag will result
in trajectories
s[0], s[lag], s[2 lag], ...
s[stride], s[stride + lag], s[stride + 2 lag], ...
Setting stride = 1 will result in using all data (useful for maximum
likelihood estimator), while a Bayesian estimator requires a longer
stride in order to have statistically uncorrelated trajectories.
Setting stride = 'effective' uses the largest neglected timescale as
an estimate for the correlation time and sets the stride accordingly
msm_init : :class:`MSM <pyemma.msm.estimators.msm_estimated.MSM>`
MSM object to initialize the estimation
reversible : bool, optional, default = True
If true compute reversible MSM, else non-reversible MSM
connectivity : str, optional, default = 'largest'
Connectivity mode. Three methods are intended (currently only 'largest' is implemented)
* 'largest' : The active set is the largest reversibly connected set. All estimation will be done on this
subset and all quantities (transition matrix, stationary distribution, etc) are only defined on this
subset and are correspondingly smaller than the full set of states
* 'all' : The active set is the full set of states. Estimation will be conducted on each reversibly
connected set separately. That means the transition matrix will decompose into disconnected
submatrices, the stationary vector is only defined within subsets, etc. Currently not implemented.
* 'none' : The active set is the full set of states. Estimation will be conducted on the full set of
states without ensuring connectivity. This only permits nonreversible estimation. Currently not
implemented.
observe_active : bool, optional, default=True
True: Restricts the observation set to the active states of the MSM.
False: All states are in the observation set.
dt_traj : str, optional, default='1 step'
Description of the physical time corresponding to the trajectory time
step. May be used by analysis algorithms such as plotting tools to
pretty-print the axes. By default '1 step', i.e. there is no physical
time unit. Specify by a number, whitespace and unit. Permitted units
are (* is an arbitrary string):
| 'fs', 'femtosecond*'
| 'ps', 'picosecond*'
| 'ns', 'nanosecond*'
| 'us', 'microsecond*'
| 'ms', 'millisecond*'
| 's', 'second*'
accuracy : float, optional, default = 1e-3
convergence threshold for EM iteration. When two the likelihood does
not increase by more than accuracy, the iteration is stopped
successfully.
maxit : int, optional, default = 1000
stopping criterion for EM iteration. When so many iterations are
performed without reaching the requested accuracy, the iteration is
stopped without convergence (a warning is given)
"""
self.nstates = nstates
self.lag = lag
self.stride = stride
self.msm_init = msm_init
self.reversible = reversible
self.connectivity = connectivity
self.observe_active = observe_active
self.dt_traj = dt_traj
self.timestep_traj = TimeUnit(dt_traj)
self.accuracy = accuracy
self.maxit = maxit
#TODO: store_data is mentioned but not implemented or used!
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
def cktest(self, mlags=10, conf=0.95, err_est=False, show_progress=True):
""" Conducts a Chapman-Kolmogorow test.
Parameters
----------
mlags : int or int-array, default=10
multiples of lag times for testing the Model, e.g. range(10).
A single int will trigger a range, i.e. mlags=10 maps to
mlags=range(10). The setting None will choose mlags automatically
according to the longest available trajectory
conf : float, optional, default = 0.95
confidence interval
err_est : bool, default=False
compute errors also for all estimations (computationally expensive)
If False, only the prediction will get error bars, which is often
sufficient to validate a model.
show_progress : bool, default=True
Show progressbars for calculation?
References
----------
This is an adaption of the Chapman-Kolmogorov Test described in detail
in [1]_ to Hidden MSMs as described in [2]_.
.. [1] Prinz, J H, H Wu, M Sarich, B Keller, M Senne, M Held, J D
Chodera, C Schuette and F Noe. 2011. Markov models of
molecular kinetics: Generation and validation. J Chem Phys
134: 174105
.. [2] F. Noe, H. Wu, J.-H. Prinz and N. Plattner: Projected and hidden
Markov models for calculating kinetics and metastable states of complex
molecules. J. Chem. Phys. 139, 184114 (2013)
"""
from pyemma.msm.estimators import ChapmanKolmogorovValidator
ck = ChapmanKolmogorovValidator(self, self, np.eye(self.nstates),
mlags=mlags, conf=conf, err_est=err_est,
show_progress=show_progress)
ck.estimate(self._dtrajs_full)
return ck