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Bayesian Nonparametric Hidden Semi-Markov Models
There is much interest in the Hierarchical Dirichlet Process Hidden Markov
Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous
Hidden Markov Model for learning from sequential and time-series data. However,
in many settings the HDP-HMM's strict Markovian constraints are undesirable,
particularly if we wish to learn or encode non-geometric state durations. We
can extend the HDP-HMM to capture such structure by drawing upon
explicit-duration semi-Markovianity, which has been developed mainly in the
parametric frequentist setting, to allow construction of highly interpretable
models that admit natural prior information on state durations.
In this paper we introduce the explicit-duration Hierarchical Dirichlet
Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for
efficient posterior inference. The methods we introduce also provide new
methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs
sampling methods can be embedded in samplers for larger hierarchical Bayesian
models, adding semi-Markov chain modeling as another tool in the Bayesian
inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference
methods on both synthetic and real experiments
Hierarchically-coupled hidden Markov models for learning kinetic rates from single-molecule data
We address the problem of analyzing sets of noisy time-varying signals that
all report on the same process but confound straightforward analyses due to
complex inter-signal heterogeneities and measurement artifacts. In particular
we consider single-molecule experiments which indirectly measure the distinct
steps in a biomolecular process via observations of noisy time-dependent
signals such as a fluorescence intensity or bead position. Straightforward
hidden Markov model (HMM) analyses attempt to characterize such processes in
terms of a set of conformational states, the transitions that can occur between
these states, and the associated rates at which those transitions occur; but
require ad-hoc post-processing steps to combine multiple signals. Here we
develop a hierarchically coupled HMM that allows experimentalists to deal with
inter-signal variability in a principled and automatic way. Our approach is a
generalized expectation maximization hyperparameter point estimation procedure
with variational Bayes at the level of individual time series that learns an
single interpretable representation of the overall data generating process.Comment: 9 pages, 5 figure
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