Decoding Coalescent Hidden Markov Models in Linear Time

AbstractHidden Markov models of haplotype inheritance such as the Li and Stephens model allow for computationally tractable probability calculations using the forward algorithms as long as the representative reference panel used in the model is sufficiently small. Specifically, the monoploid Li and Stephens model and its variants are linear in reference panel size unless heuristic approximations are used. However, sequencing projects numbering in the thousands to hundreds of thousands of individuals are underway, and others numbering in the millions are anticipated.To make the Li and Stephens forward algorithm for these datasets computationally tractable, we have created a numerically exact version of the algorithm with observed average case 𝒪(nk0.35) runtime, avoiding any tradeoff between runtime and model complexity. We demonstrate that our approach also provides a succinct data structure for general purpose haplotype data storage. We discuss generalizations of our algorithmic techniques to other hidden Markov models.2012 ACM Subject ClassificationTheory of computation ⟶ Streaming, sublinear and near linear time algorithms; Applied computing ⟶ BioinformaticsSupplement Materialhttps://github.com/yoheirosen/sublinear-Li-Stephens.FundingThis work was supported by the National Human Genome Research Institute of the National Institutes of Health under Award Number 5U54HG007990, the National Heart, Lung, and Blood Institute of the National Institutes of Health under Award Number 1U01HL137183-01, and grants from the W.M. Keck foundation and the Simons Foundation.AcknowledgementsWe would like to thank Jordan Eizenga for his helpful discussions throughout the development of this work.

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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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