scholarly journals Exact inference for a class of hidden Markov models on general state spaces

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Guillaume Kon Kam King ◽  
Omiros Papaspiliopoulos ◽  
Matteo Ruggiero
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
General State ◽  
State Spaces ◽  
Exact Inference

scholarly journals FactorialHMM: Fast and exact inference in factorial hidden Markov models

2018 ◽  
Author(s):  
Regev Schweiger ◽  
Yaniv Erlich ◽  
Shai Carmi
Keyword(s):  
Hidden Markov Models ◽  
Posterior Probability ◽  
Markov Models ◽  
Hidden Markov ◽  
Cartesian Product ◽  
Exact Inference ◽  
Running Time ◽  
Time Scaling ◽  
Multiple Processes ◽  
Hidden States

MotivationHidden Markov models (HMMs) are powerful tools for modeling processes along the genome. In a standard genomic HMM, observations are drawn, at each genomic position, from a distribution whose parameters depend on a hidden state; the hidden states evolve along the genome as a Markov chain. Often, the hidden state is the Cartesian product of multiple processes, each evolving independently along the genome. Inference in these so-called Factorial HMMs has a naïve running time that scales as the square of the number of possible states, which by itself increases exponentially with the number of subchains; such a running time scaling is impractical for many applications. While faster algorithms exist, there is no available implementation suitable for developing bioinformatics applications.ResultsWe developed FactorialHMM, a Python package for fast exact inference in Factorial HMMs. Our package allows simulating either directly from the model or from the posterior distribution of states given the observations. Additionally, we allow the inference of all key quantities related to HMMs: (1) the (Viterbi) sequence of states with the highest posterior probability; (2) the likelihood of the data; and (3) the posterior probability (given all observations) of the marginal and pairwise state probabilities. The running time and space requirement of all procedures is linearithmic in the number of possible states. Our package is highly modular, providing the user with maximal flexibility for developing downstream applications.Availabilityhttps://github.com/regevs/factorialhmm

AN INTRODUCTION TO HIDDEN MARKOV MODELS AND BAYESIAN NETWORKS

2001 ◽  
Vol 15 (01) ◽  
pp. 9-42 ◽  
Author(s):  
ZOUBIN GHAHRAMANI
Keyword(s):  
Bayesian Networks ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Recent Literature ◽  
Hidden Markov ◽  
Continuous Variables ◽  
State Variables ◽  
Exact Inference ◽  
Markov Chain Sampling ◽  
Inference Algorithms

We provide a tutorial on learning and inference in hidden Markov models in the context of the recent literature on Bayesian networks. This perspective makes it possible to consider novel generalizations of hidden Markov models with multiple hidden state variables, multiscale representations, and mixed discrete and continuous variables. Although exact inference in these generalizations is usually intractable, one can use approximate inference algorithms such as Markov chain sampling and variational methods. We describe how such methods are applied to these generalized hidden Markov models. We conclude this review with a discussion of Bayesian methods for model selection in generalized HMMs.

scholarly journals Sequential Monte Carlo smoothing for general state space hidden Markov models

2011 ◽  
Vol 21 (6) ◽  
pp. 2109-2145 ◽  
Author(s):  
Randal Douc ◽  
Aurélien Garivier ◽  
Eric Moulines ◽  
Jimmy Olsson
Keyword(s):  
Monte Carlo ◽  
State Space ◽  
Hidden Markov Models ◽  
Sequential Monte Carlo ◽  
Markov Models ◽  
Hidden Markov ◽  
General State ◽  
General State Space

scholarly journals Finite State-Spaces and Hidden Markov Models

2020 ◽  
pp. 67-71
Author(s):  
Nicolas Chopin ◽  
Omiros Papaspiliopoulos
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
State Spaces ◽  
Finite State

HMM with emission process resulting from a special combination of independent Markovian emissions

2017 ◽  
Vol 23 (4) ◽  
Author(s):  
Abdelaziz Nasroallah ◽  
Karima Elkimakh
Keyword(s):  
Markov Chains ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
The State ◽  
State Spaces ◽  
Standard Case ◽  
Emission Process

AbstractOne of the most used variants of hidden Markov models (HMMs) is the standard case where the time is discrete and the state spaces (hidden and observed spaces) are finite. In this framework, we are interested in HMMs whose emission process results from a combination of independent Markov chains. Principally, we assume that the emission process evolves as follows: given a hidden state realization

scholarly journals FactorialHMM: fast and exact inference in factorial hidden Markov models

2018 ◽  
Vol 35 (12) ◽  
pp. 2162-2164
Author(s):  
Regev Schweiger ◽  
Yaniv Erlich ◽  
Shai Carmi
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Exact Inference ◽  
Factorial Hidden Markov Models

scholarly journals Big Data Analysis of Electronic Health Records: Clinically interpretable representations of older adult inpatient trajectories using time-series numerical data and Hidden Markov Models

2021 ◽  
Author(s):  
Maria Herrero-Zazo ◽  
Victoria L Keevil ◽  
Vince Taylor ◽  
Helen Street ◽  
Afzal N Chaudhry ◽  
...  
Keyword(s):  
Time Series ◽  
Big Data ◽  
Data Analysis ◽  
Electronic Health Records ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Big Data Analysis ◽  
Health Records ◽  
State Spaces

The implementation of Electronic Health Records (EHR) in UK hospitals provides new opportunities for clinical 'big data' analysis. The representation of observations routinely recorded in clinical practice is the first step to use these data in several research tasks. Anonymised data were extracted from 11 158 first emergency admission episodes (AE) in older adults. Irregular records from 23 laboratory blood tests and vital signs were normalized and regularised into daily bins and represented as numerical multivariate time-series (MVTS). Unsupervised Hidden Markov Models (HMM) were trained to represent each day of each AE as one of 17 state spaces. The visual clinical interpretation of these states showed remarkable differences between patients who died at the end of the AE and those who were discharged. All states had marked features that allowed their clinical interpretation and differentiation between those associated with the patients' disease burden, their physiological response to this burden or the stage of admission. The most evident relationships with hold-out clinical information were also confirmed by Chi-square tests, with two states strongly associated with inpatient mortality (IM) and 12 states (71%) associated with at least one admission diagnosis. The potential of these data representations on prediction of hospital outcomes was also explored using Logistic Regression (LR) and Random Forest (RF) models, with higher prediction performance observed when models were trained with MVTS data compared to HMM state spaces. However, the outputs of generative and discriminative analyses were complementary. For example, highest ranking features of the best performing RF model for IM (ROC-AUC 0.851) resembled the laboratory blood test and vital sign variables characterising the 'Early Inflammatory Response-like' state, itself strongly associated with IM. These results provide evidence of the capability of generative models to extract biological signals from routinely collected clinical data and their potential to represent interpretable patients' trajectories for future research in hypothesis generation or prediction modelling.

Estimating Personality Impression from Speech Record Using Hidden Markov Models

2015 ◽  
Vol 135 (12) ◽  
pp. 1517-1523 ◽  
Author(s):  
Yicheng Jin ◽  
Takuto Sakuma ◽  
Shohei Kato ◽  
Tsutomu Kunitachi
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov

Hidden Markov Processes

2014 ◽  
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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