class HiddenMarkovModel¶

class deeptime.markov.hmm.HiddenMarkovModel(transition_model, output_model: Union[ndarray, OutputModel], initial_distribution: Optional[ndarray] = None, likelihoods: Optional[ndarray] = None, state_probabilities: Optional[List[ndarray]] = None, initial_count: Optional[ndarray] = None, hidden_state_trajectories: Optional[Iterable[ndarray]] = None, stride: Union[int, str] = 1, observation_symbols: Optional[ndarray] = None, observation_symbols_full: Optional[ndarray] = None)¶

Hidden Markov state model consisting of a transition model (MSM) on the hidden states, an output model which maps from the hidden states to a distribution of observable states, and optionally an initial distribution on the hidden states. Some properties require a crisp assignment to states in the observable space, in which case only a discrete output model can be used.

Parameters:

transition_model ((m,m) ndarray or MarkovStateModel) – Transition matrix for hidden (macro) states
output_model ((m,n) ndarray or OutputModel) – observation probability matrix from hidden to observable (micro) states or OutputModel instance which yields the mapping from hidden to observable state.
initial_distribution ((m,) ndarray, optional, default=None) – Initial distribution of the hidden (macro) states. Default is uniform.
likelihoods ((k,) ndarray, optional, default=None) – Likelihood progression of the HMM as it was trained for k iterations with Baum-Welch.
state_probabilities (list of ndarray, optional, default=None) – List of state probabilities for each trajectory that the model was trained on (gammas).
initial_count (ndarray, optional, default=None) – Initial counts of the hidden (macro) states, computed from the gamma output of the Baum-Welch algorithm
hidden_state_trajectories (list of ndarray, optional, default=None) – When estimating the HMM the data’s most likely hidden state trajectory is determined and can be saved with the model by providing this argument.
stride (int or str('effective'), optional, default=1) – Stride which was used to subsample discrete trajectories while estimating a HMM. Can either be an integer value which determines the offset or ‘effective’, which makes an estimate of a stride at which subsequent discrete trajectory elements are uncorrelated.
observation_symbols (array_like, optional, default=None) – Sorted unique symbols in observations. If None, it is assumed that all possible observations are made and the state symbols are set to an iota range over the number of observation states.
observation_symbols_full (array_like, optional, default=None) – Full set of symbols in observations. If None, it is assumed to coincide with observation_symbols.

References

[1] (1,2,3)

Frank Noé, Hao Wu, Jan-Hendrik Prinz, and Nuria Plattner. Projected and hidden markov models for calculating kinetics and metastable states of complex molecules. The Journal of chemical physics, 139(18):11B609_1, 2013.

`count_model`	Yields the count model for the micro (hidden) states.
`eigenvectors_left_obs`	Left eigenvectors in observation space.
`eigenvectors_right_obs`	Right eigenvectors in observation space.
`hidden_state_trajectories`	Training trajectories mapped to hidden states after estimation.
`initial_count`	The hidden initial counts, can be None.
`initial_distribution`	The initial distribution of this HMM over the hidden states.
`lagtime`	The lagtime this model was estimated at.
`lifetimes`	Lifetimes of states of the hidden transition matrix
`likelihood`	The estimated likelihood of this model based on the training data.
`likelihoods`	If the model comes from the MaximumLikelihoodHMM estimator, this property contains the sequence of likelihoods generated from the fitting iteration.
`metastable_assignments`	Computes the assignment to metastable sets for observable states
`metastable_distributions`	Returns the output probability distributions. Identical to
`metastable_memberships`	Computes the memberships of observable states to metastable sets by Bayesian inversion.
`metastable_sets`	Computes the metastable sets of observable states within each
`n_hidden_states`	The number of hidden states.
`n_observation_states`	Property determining the number of observed/macro states.
`observation_symbols`	The symbols represented by this HMM in observation space.
`observation_symbols_full`	All symbols that the original model contained (original before taking any submodel).
`output_model`	The selected output model for this HMM.
`output_probabilities`	Returns the probabilities for each hidden state to map to a particular observation state.
`state_probabilities`	List of state probabilities for each trajectory that the model was trained on (gammas in the Baum-Welch algo).
`stationary_distribution_obs`	The stationary distribution in observable space.
`stride`	The stride parameter which was used to subsample the discrete trajectories when estimating the hidden markov state model.
`transition_counts`	The transition counts for the hidden states as estimated in the fitting procedure.
`transition_model`	Yields the transition model for the hidden states.

`ck_test`(models[, include_lag0, err_est, ...])	Performs a Chapman-Kolmogorov test on a list of HMMs.
`collect_observations_in_state`(observations, ...)	Collect a vector of all observations belonging to a specified hidden state.
`compute_observation_likelihood`(data)	Computes the likelihood of observed data under this model.
`compute_viterbi_paths`(observations[, ...])	Computes the Viterbi paths using the current HMM model.
`copy`()	Makes a deep copy of this model.
`correlation_obs`(a[, b, maxtime, k, ncv])	Time-correlation for equilibrium experiment based on observable state vectors a and b.
`expectation_obs`(a)	Equilibrium expectation value of a given observable state vector.
`fingerprint_correlation_obs`(a[, b, k, ncv])	Dynamical fingerprint for equilibrium time-correlation experiment based on observable state vectors a and b.
`fingerprint_relaxation_obs`(p0, a[, k, ncv])	Dynamical fingerprint for perturbation/relaxation experiment based on observable state vector and distribution.
`get_params`([deep])	Get the parameters.
`nonempty_obs`(dtrajs)	Computes the set of visited observable states given a set of discrete trajectories.
`propagate`(p0, k)	Propagates the initial distribution p0 defined on observable space k times.
`relaxation_obs`(p0, a[, maxtime, k, ncv])	Simulates a perturbation-relaxation experiment based on observable state vector and distribution.
`sample_by_observation_probabilities`(dtrajs, ...)	Generates samples according to the current observation probability distribution.
`set_params`(**params)	Set the parameters of this estimator.
`simulate`(n_steps[, start, stop, dt])	Generates a realization of the Hidden Markov Model
`states_largest`([directed, ...])	Selects hidden states which represent the largest connected set.
`states_populous`([strong, connectivity_threshold])	Retrieves the hidden states which are most populated and connected.
`submodel`([states, obs])	Returns a HMM with restricted state space
`submodel_disconnect`([connectivity_threshold])	Disconnects sets of hidden states that are barely connected
`submodel_largest`([directed, ...])	Returns the largest connected sub-HMM.
`submodel_populous`([directed, ...])	Returns the most populous connected sub-HMM.
`timescales`([k])	Yields the timescales of the hidden transition model.
`transform_discrete_trajectories_to_observed_symbols`(dtrajs)	A list of integer arrays with the discrete trajectories mapped to the currently used set of observation symbols.
`transition_matrix_obs`([k])	Computes the transition matrix between observed states