Algorithms for a Parallel Implementation of Hidden Markov Models with a Small State Space

We introduce a new statistical model for time series that iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time-series models—hidden Markov models and linear dynamical systems—and is closely related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network (Jacobs, Jordan, Nowlan, & Hinton, 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact expectation maximization (EM) algorithm cannot be applied. However, we present a variational approximation that maximizes a lower bound on the log-likelihood and makes use of both the forward and backward recursions for hidden Markov models and the Kalman filter recursions for linear dynamical systems. We tested the algorithm on artificial data sets and a natural data set of respiration force from a patient with sleep apnea. The results suggest that variational approximations are a viable method for inference and learning in switching state-space models.

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Estimating Personality Impression from Speech Record Using Hidden Markov Models

IEEJ Transactions on Electronics Information and Systems ◽

10.1541/ieejeiss.135.1517 ◽

2015 ◽

Vol 135 (12) ◽

pp. 1517-1523 ◽

Cited By ~ 1

Author(s):

Yicheng Jin ◽

Takuto Sakuma ◽

Shohei Kato ◽

Tsutomu Kunitachi

Keyword(s):

Hidden Markov Models ◽

Markov Models ◽

Hidden Markov

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Hidden Markov Processes

10.23943/princeton/9780691133157.001.0001 ◽

2014 ◽

Cited By ~ 2

Author(s):

M. Vidyasagar

Keyword(s):

Hidden Markov Models ◽

Markov Processes ◽

Viterbi Algorithm ◽

Markov Models ◽

Hidden Markov ◽

Local Alignment ◽

Biological Applications ◽

Standard Material ◽

Hidden Markov Processes ◽

Genomics And Proteomics

This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. It starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are taken from post-genomic biology, especially genomics and proteomics. The topics examined include standard material such as the Perron–Frobenius theorem, transient and recurrent states, hitting probabilities and hitting times, maximum likelihood estimation, the Viterbi algorithm, and the Baum–Welch algorithm. The book contains discussions of extremely useful topics not usually seen at the basic level, such as ergodicity of Markov processes, Markov Chain Monte Carlo (MCMC), information theory, and large deviation theory for both i.i.d and Markov processes. It also presents state-of-the-art realization theory for hidden Markov models. Among biological applications, it offers an in-depth look at the BLAST (Basic Local Alignment Search Technique) algorithm, including a comprehensive explanation of the underlying theory. Other applications such as profile hidden Markov models are also explored.

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