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