Revealing Ensemble State Transition Patterns in Multi-Electrode Neuronal Recordings Using Hidden Markov Models

Neural activity is nonstationary and varies across time. Hidden Markov models (HMMs) have been used to track the state transition among quasi-stationary discrete neural states. Within this context, an independent Poisson model has been used for the output distribution of HMMs; hence, the model is incapable of tracking the change in correlation without modulating the firing rate. To achieve this, we applied a multivariate Poisson distribution with correlation terms for the output distribution of HMMs. We formulated a variational Bayes (VB) inference for the model. The VB could automatically determine the appropriate number of hidden states and correlation types while avoiding the overlearning problem. We developed an efficient algorithm for computing posteriors using the recursive relationship of a multivariate Poisson distribution. We demonstrated the performance of our method on synthetic data and real spike trains recorded from a songbird.

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Equivalence of Linear Boltzmann Chains and Hidden Markov Models

Neural Computation ◽

10.1162/neco.1996.8.1.178 ◽

1996 ◽

Vol 8 (1) ◽

pp. 178-181 ◽

Cited By ~ 8

Author(s):

David J. C. MacKay

Keyword(s):

Probability Distribution ◽

Markov Model ◽

Hidden Markov Models ◽

State Transition ◽

Markov Models ◽

Hidden Markov ◽

Simple Condition ◽

Transition Energies ◽

State Sequence ◽

The Relationship

Several authors have studied the relationship between hidden Markov models and “Boltzmann chains” with a linear or “time-sliced” architecture. Boltzmann chains model sequences of states by defining state-state transition energies instead of probabilities. In this note I demonstrate that under the simple condition that the state sequence has a mandatory end state, the probability distribution assigned by a strictly linear Boltzmann chain is identical to that assigned by a hidden Markov model.

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Metal Label Pressed Protuberant Characters Recognition Based on Hidden Markov Model

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.187.667 ◽

2011 ◽

Vol 187 ◽

pp. 667-671

Author(s):

Wei Chen

Keyword(s):

Neural Network ◽

Markov Model ◽

Hidden Markov Models ◽

State Transition ◽

Markov Models ◽

Hidden Markov ◽

Shape Index ◽

Surface Curvature ◽

Word Choice ◽

Recognition Method

A recognition method of pressed protuberant characters based on Hidden Markov models and Neural Network is applied, which the surface curvature properties and the relation of metal label characters are analyzed in detail. The shape index of the characters is extracted. A neural network is used to estimate probabilities for the characters depended on the surface curvature properties, then deriving the best word choice from a sequence of state transition. It is shown in test that the proposed method can be used to recognize the pressed protuberant on metal label.

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Worth the effort? A practical examination of random effects in hidden Markov models for animal telemetry data

10.1101/2020.07.10.196410 ◽

2020 ◽

Author(s):

Brett T. McClintock

Keyword(s):

Hidden Markov Models ◽

Random Effects ◽

State Transition ◽

Markov Models ◽

Transition Probabilities ◽

Hidden Markov ◽

Random Effect ◽

Costs And Benefits ◽

State Process ◽

Random Effect Models

AbstractHidden Markov models (HMMs) that include individual-level random effects have recently been promoted for inferring animal movement behaviour from biotelemetry data. These “mixed HMMs” come at significant cost in terms of implementation and computation, and discrete random effects have been advocated as a practical alternative to more computationally-intensive continuous random effects. However, the performance of mixed HMMs has not yet been sufficiently explored to justify their widespread adoption, and there is currently little guidance for practitioners weighing the costs and benefits of mixed HMMs for a particular research objective.I performed an extensive simulation study comparing the performance of a suite of fixed and random effect models for individual heterogeneity in the hidden state process of a 2-state HMM. I focused on sampling scenarios more typical of telemetry studies, which often consist of relatively long time series (30 – 250 observations per animal) for relatively few individuals (5 – 100 animals).I generally found mixed HMMs did not improve state assignment relative to standard HMMs. Reliable estimation of random effects required larger sample sizes than are often feasible in telemetry studies. Continuous random effect models performed reasonably well with data generated under discrete random effects, but not vice versa. Random effects accounting for unexplained individual variation can improve estimation of state transition probabilities and measurable covariate effects, but discrete random effects can be a relatively poor (and potentially misleading) approximation for continuous variation.When weighing the costs and benefits of mixed HMMs, three important considerations are study objectives, sample size, and model complexity. HMM applications often focus on state assignment with little emphasis on heterogeneity in state transition probabilities, in which case random effects in the hidden state process simply may not be worth the additional effort. However, if explaining variation in state transition probabilities is a primary objective and sufficient explanatory covariates are not available, then random effects are worth pursuing as a more parsimonious alternative to individual fixed effects.To help put my findings in context and illustrate some potential challenges that practitioners may encounter when applying mixed HMMs, I revisit a previous analysis of long-finned pilot whale biotelemetry data.

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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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