def bayesian_hmm(observations, estimated_hmm, nsample=100, transition_matrix_prior=None,
store_hidden=False, call_back=None):
r""" Bayesian HMM based on sampling the posterior
Generic maximum-likelihood estimation of HMMs
Parameters
----------
observations : list of numpy arrays representing temporal data
`observations[i]` is a 1d numpy array corresponding to the observed trajectory index `i`
estimated_hmm : HMM
HMM estimated from estimate_hmm or initialize_hmm
nsample : int, optional, default=100
number of Gibbs sampling steps
transition_matrix_prior : str or ndarray(n,n)
prior count matrix to be used for transition matrix sampling, or a keyword specifying the prior mode
| None (default), -1 prior is used that ensures consistency between mean and MLE. Can lead to sampling
disconnected matrices in the low-data regime. If you have disconnectivity problems, consider
using 'init-connect'
| 'init-connect', prior count matrix ensuring the same connectivity as in the initial model. 1 count
is added to all diagonals. All off-diagonals share one prior count distributed proportional to
the row of the initial transition matrix.
store_hidden : bool, optional, default=False
store hidden trajectories in sampled HMMs
call_back : function, optional, default=None
a call back function with no arguments, which if given is being called
after each computed sample. This is useful for implementing progress bars.
Return
------
hmm : :class:`SampledHMM <bhmm.hmm.generic_sampled_hmm.SampledHMM>`
"""
# construct estimator
from bhmm.estimators.bayesian_sampling import BayesianHMMSampler as _BHMM
sampler = _BHMM(observations, estimated_hmm.nstates, initial_model=estimated_hmm,
reversible=estimated_hmm.is_reversible, transition_matrix_sampling_steps=1000,
transition_matrix_prior=transition_matrix_prior, type=estimated_hmm.output_model.model_type)
# Sample models.
sampled_hmms = sampler.sample(nsamples=nsample, save_hidden_state_trajectory=store_hidden,
call_back=call_back)
# return model
from bhmm.hmm.generic_sampled_hmm import SampledHMM
return SampledHMM(estimated_hmm, sampled_hmms)
def bayesian_hmm(observations, estimated_hmm, nsample=100, reversible=True, stationary=False,
p0_prior='mixed', transition_matrix_prior='mixed', store_hidden=False, call_back=None):
r""" Bayesian HMM based on sampling the posterior
Generic maximum-likelihood estimation of HMMs
Parameters
----------
observations : list of numpy arrays representing temporal data
`observations[i]` is a 1d numpy array corresponding to the observed trajectory index `i`
estimated_hmm : HMM
HMM estimated from estimate_hmm or initialize_hmm
reversible : bool, optional, default=True
If True, a prior that enforces reversible transition matrices (detailed balance) is used;
otherwise, a standard non-reversible prior is used.
stationary : bool, optional, default=False
If True, the stationary distribution of the transition matrix will be used as initial distribution.
Only use True if you are confident that the observation trajectories are started from a global
equilibrium. If False, the initial distribution will be estimated as usual from the first step
of the hidden trajectories.
nsample : int, optional, default=100
number of Gibbs sampling steps
p0_prior : None, str, float or ndarray(n)
Prior for the initial distribution of the HMM. Will only be active
if stationary=False (stationary=True means that p0 is identical to
the stationary distribution of the transition matrix).
Currently implements different versions of the Dirichlet prior that
is conjugate to the Dirichlet distribution of p0. p0 is sampled from:
.. math:
p0 \sim \prod_i (p0)_i^{a_i + n_i - 1}
where :math:`n_i` are the number of times a hidden trajectory was in
state :math:`i` at time step 0 and :math:`a_i` is the prior count.
Following options are available:
| 'mixed' (default), :math:`a_i = p_{0,init}`, where :math:`p_{0,init}`
is the initial distribution of initial_model.
| 'uniform', :math:`a_i = 1`
| ndarray(n) or float,
the given array will be used as A.
| None, :math:`a_i = 0`. This option ensures coincidence between
sample mean an MLE. Will sooner or later lead to sampling problems,
because as soon as zero trajectories are drawn from a given state,
the sampler cannot recover and that state will never serve as a starting
state subsequently. Only recommended in the large data regime and
when the probability to sample zero trajectories from any state
is negligible.
transition_matrix_prior : str or ndarray(n, n)
Prior for the HMM transition matrix.
Currently implements Dirichlet priors if reversible=False and reversible
transition matrix priors as described in [1]_ if reversible=True. For the
nonreversible case the posterior of transition matrix :math:`P` is:
.. math:
P \sim \prod_{i,j} p_{ij}^{b_{ij} + c_{ij} - 1}
where :math:`c_{ij}` are the number of transitions found for hidden
trajectories and :math:`b_{ij}` are prior counts.
| 'mixed' (default), :math:`b_{ij} = p_{ij,init}`, where :math:`p_{ij,init}`
is the transition matrix of initial_model. That means one prior
count will be used per row.
| 'uniform', :math:`b_{ij} = 1`
| ndarray(n, n) or broadcastable,
the given array will be used as B.
| None, :math:`b_ij = 0`. This option ensures coincidence between
sample mean an MLE. Will sooner or later lead to sampling problems,
because as soon as a transition :math:`ij` will not occur in a
sample, the sampler cannot recover and that transition will never
be sampled again. This option is not recommended unless you have
a small HMM and a lot of data.
store_hidden : bool, optional, default=False
store hidden trajectories in sampled HMMs
call_back : function, optional, default=None
a call back function with no arguments, which if given is being called
after each computed sample. This is useful for implementing progress bars.
Return
------
hmm : :class:`SampledHMM <bhmm.hmm.generic_sampled_hmm.SampledHMM>`
References
----------
.. [1] Trendelkamp-Schroer, B., H. Wu, F. Paul and F. Noe:
Estimation and uncertainty of reversible Markov models.
J. Chem. Phys. 143, 174101 (2015).
"""
# construct estimator
from bhmm.estimators.bayesian_sampling import BayesianHMMSampler as _BHMM
sampler = _BHMM(observations, estimated_hmm.nstates, initial_model=estimated_hmm,
reversible=reversible, stationary=stationary, transition_matrix_sampling_steps=1000,
p0_prior=p0_prior, transition_matrix_prior=transition_matrix_prior,
output=estimated_hmm.output_model.model_type)
# Sample models.
sampled_hmms = sampler.sample(nsamples=nsample, save_hidden_state_trajectory=store_hidden,
call_back=call_back)
# return model
from bhmm.hmm.generic_sampled_hmm import SampledHMM
return SampledHMM(estimated_hmm, sampled_hmms)
def bayesian_hmm(observations,
estimated_hmm,
nsample=100,
reversible=True,
stationary=False,
p0_prior='mixed',
transition_matrix_prior='mixed',
store_hidden=False,
call_back=None):
r""" Bayesian HMM based on sampling the posterior
Generic maximum-likelihood estimation of HMMs
Parameters
----------
observations : list of numpy arrays representing temporal data
`observations[i]` is a 1d numpy array corresponding to the observed trajectory index `i`
estimated_hmm : HMM
HMM estimated from estimate_hmm or initialize_hmm
reversible : bool, optional, default=True
If True, a prior that enforces reversible transition matrices (detailed balance) is used;
otherwise, a standard non-reversible prior is used.
stationary : bool, optional, default=False
If True, the stationary distribution of the transition matrix will be used as initial distribution.
Only use True if you are confident that the observation trajectories are started from a global
equilibrium. If False, the initial distribution will be estimated as usual from the first step
of the hidden trajectories.
nsample : int, optional, default=100
number of Gibbs sampling steps
p0_prior : None, str, float or ndarray(n)
Prior for the initial distribution of the HMM. Will only be active
if stationary=False (stationary=True means that p0 is identical to
the stationary distribution of the transition matrix).
Currently implements different versions of the Dirichlet prior that
is conjugate to the Dirichlet distribution of p0. p0 is sampled from:
.. math:
p0 \sim \prod_i (p0)_i^{a_i + n_i - 1}
where :math:`n_i` are the number of times a hidden trajectory was in
state :math:`i` at time step 0 and :math:`a_i` is the prior count.
Following options are available:
| 'mixed' (default), :math:`a_i = p_{0,init}`, where :math:`p_{0,init}`
is the initial distribution of initial_model.
| 'uniform', :math:`a_i = 1`
| ndarray(n) or float,
the given array will be used as A.
| None, :math:`a_i = 0`. This option ensures coincidence between
sample mean an MLE. Will sooner or later lead to sampling problems,
because as soon as zero trajectories are drawn from a given state,
the sampler cannot recover and that state will never serve as a starting
state subsequently. Only recommended in the large data regime and
when the probability to sample zero trajectories from any state
is negligible.
transition_matrix_prior : str or ndarray(n, n)
Prior for the HMM transition matrix.
Currently implements Dirichlet priors if reversible=False and reversible
transition matrix priors as described in [1]_ if reversible=True. For the
nonreversible case the posterior of transition matrix :math:`P` is:
.. math:
P \sim \prod_{i,j} p_{ij}^{b_{ij} + c_{ij} - 1}
where :math:`c_{ij}` are the number of transitions found for hidden
trajectories and :math:`b_{ij}` are prior counts.
| 'mixed' (default), :math:`b_{ij} = p_{ij,init}`, where :math:`p_{ij,init}`
is the transition matrix of initial_model. That means one prior
count will be used per row.
| 'uniform', :math:`b_{ij} = 1`
| ndarray(n, n) or broadcastable,
the given array will be used as B.
| None, :math:`b_ij = 0`. This option ensures coincidence between
sample mean an MLE. Will sooner or later lead to sampling problems,
because as soon as a transition :math:`ij` will not occur in a
sample, the sampler cannot recover and that transition will never
be sampled again. This option is not recommended unless you have
a small HMM and a lot of data.
store_hidden : bool, optional, default=False
store hidden trajectories in sampled HMMs
call_back : function, optional, default=None
a call back function with no arguments, which if given is being called
after each computed sample. This is useful for implementing progress bars.
Return
------
hmm : :class:`SampledHMM <bhmm.hmm.generic_sampled_hmm.SampledHMM>`
References
----------
.. [1] Trendelkamp-Schroer, B., H. Wu, F. Paul and F. Noe:
Estimation and uncertainty of reversible Markov models.
J. Chem. Phys. 143, 174101 (2015).
"""
# construct estimator
from bhmm.estimators.bayesian_sampling import BayesianHMMSampler as _BHMM
sampler = _BHMM(observations,
estimated_hmm.nstates,
initial_model=estimated_hmm,
reversible=reversible,
stationary=stationary,
transition_matrix_sampling_steps=1000,
p0_prior=p0_prior,
transition_matrix_prior=transition_matrix_prior,
output=estimated_hmm.output_model.model_type)
# Sample models.
sampled_hmms = sampler.sample(nsamples=nsample,
save_hidden_state_trajectory=store_hidden,
call_back=call_back)
# return model
from bhmm.hmm.generic_sampled_hmm import SampledHMM
return SampledHMM(estimated_hmm, sampled_hmms)
