scholarly journals Bayesian selection of Hidden Markov models for multi-dimensional ion channel data

2020 ◽  
Author(s):  
Jan Münch ◽  
Fabian Paul ◽  
Ralf Schmauder ◽  
Klaus Benndorf
Keyword(s):  
Hidden Markov Models ◽  
Cross Validation ◽  
Markov Models ◽  
Hidden Markov ◽  
Conformational Dynamics ◽  
Kinetic Scheme ◽  
Rate Equations ◽  
Model Parameters ◽  
Limited Information ◽  
Daunting Task

AbstractInferring the complex conformational dynamics of ion channels from ensemble currents is a daunting task due to limited information in the data leading to poorly determined model inference and selection. We address this problem with a parallelized Kalman filter for specifying Hidden Markov Models for current and fluorescence data. We demonstrate the flexibility of this Bayesian network by including different noises distributions. The accuracy of the parameter estimation is increased by tenfold compared to fitting Rate Equations. Furthermore, adding orthogonal fluorescence data increases the accuracy of the model parameters by up to two orders of magnitude. Additional prior information alleviates parameter unidenfiability for weakly informative data. We show that with Rate Equations a reliable detection of the true kinetic scheme requires cross validation. In contrast, our algorithm avoids overfitting by automatically switching of rates (continuous model expansion), by cross-validation, by applying the ‘widely applicable information criterion’ or variance-based model selection.

scholarly journals Handling underlying discrete variables with bivariate mixed hidden Markov models in NONMEM

2019 ◽  
Vol 46 (6) ◽  
pp. 591-604 ◽  
Author(s):  
A. Brekkan ◽  
S. Jönsson ◽  
M. O. Karlsson ◽  
E. L. Plan
Keyword(s):  
Hidden Markov Models ◽  
Transition Rate ◽  
Markov Models ◽  
Drug Effect ◽  
Hidden Markov ◽  
Transition Probability ◽  
Hidden Variables ◽  
Model Parameters ◽  
Patient Reported ◽  
Parameter Precision

Abstract Non-linear mixed effects models typically deal with stochasticity in observed processes but models accounting for only observed processes may not be the most appropriate for all data. Hidden Markov models (HMMs) characterize the relationship between observed and hidden variables where the hidden variables can represent an underlying and unmeasurable disease status for example. Adding stochasticity to HMMs results in mixed HMMs (MHMMs) which potentially allow for the characterization of variability in unobservable processes. Further, HMMs can be extended to include more than one observation source and are then multivariate HMMs. In this work MHMMs were developed and applied in a chronic obstructive pulmonary disease example. The two hidden states included in the model were remission and exacerbation and two observation sources were considered, patient reported outcomes (PROs) and forced expiratory volume (FEV1). Estimation properties in the software NONMEM of model parameters were investigated with and without random and covariate effect parameters. The influence of including random and covariate effects of varying magnitudes on the parameters in the model was quantified and a power analysis was performed to compare the power of a single bivariate MHMM with two separate univariate MHMMs. A bivariate MHMM was developed for simulating and analysing hypothetical COPD data consisting of PRO and FEV1 measurements collected every week for 60 weeks. Parameter precision was high for all parameters with the exception of the variance of the transition rate dictating the transition from remission to exacerbation (relative root mean squared error [RRMSE] > 150%). Parameter precision was better with higher magnitudes of the transition probability parameters. A drug effect was included on the transition rate probability and the precision of the drug effect parameter improved with increasing magnitude of the parameter. The power to detect the drug effect was improved by utilizing a bivariate MHMM model over the univariate MHMM models where the number of subject required for 80% power was 25 with the bivariate MHMM model versus 63 in the univariate MHMM FEV1 model and > 100 in the univariate MHMM PRO model. The results advocates for the use of bivariate MHMM models when implementation is possible.

Online Learning with Hidden Markov Models

2008 ◽  
Vol 20 (7) ◽  
pp. 1706-1716 ◽  
Author(s):  
Gianluigi Mongillo ◽  
Sophie Deneve
Keyword(s):  
Em Algorithm ◽  
Hidden Markov Models ◽  
Online Algorithm ◽  
Markov Models ◽  
Hidden Markov ◽  
Parameters Estimation ◽  
Discount Factor ◽  
Model Parameters ◽  
Sufficient Statistics ◽  
Backward Procedure

We present an online version of the expectation-maximization (EM) algorithm for hidden Markov models (HMMs). The sufficient statistics required for parameters estimation is computed recursively with time, that is, in an online way instead of using the batch forward-backward procedure. This computational scheme is generalized to the case where the model parameters can change with time by introducing a discount factor into the recurrence relations. The resulting algorithm is equivalent to the batch EM algorithm, for appropriate discount factor and scheduling of parameters update. On the other hand, the online algorithm is able to deal with dynamic environments, i.e., when the statistics of the observed data is changing with time. The implications of the online algorithm for probabilistic modeling in neuroscience are briefly discussed.

scholarly journals Characterizing infectious disease progression through discrete states using hidden Markov models

PLoS ONE ◽  
2020 ◽  
Vol 15 (11) ◽  
pp. e0242683
Author(s):  
Kristina M. Ceres ◽  
Ynte H. Schukken ◽  
Yrjö T. Gröhn
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Disease Progression ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Clinical Signs ◽  
Disease State ◽  
Clinical Disease ◽  
Model Parameters

Infectious disease management relies on accurate characterization of disease progression so that transmission can be prevented. Slowly progressing infectious diseases can be difficult to characterize because of a latency period between the time an individual is infected and when they show clinical signs of disease. The introduction of Mycobacterium avium ssp. paratuberculosis (MAP), the cause of Johne’s disease, onto a dairy farm could be undetected by farmers for years before any animal shows clinical signs of disease. In this time period infected animals may shed thousands of colony forming units. Parameterizing trajectories through disease states from infection to clinical disease can help farmers to develop control programs based on targeting individual disease state, potentially reducing both transmission and production losses due to disease. We suspect that there are two distinct progression pathways; one where animals progress to a high-shedding disease state, and another where animals maintain a low-level of shedding without clinical disease. We fit continuous-time hidden Markov models to multi-year longitudinal fecal sampling data from three US dairy farms, and estimated model parameters using a modified Baum-Welch expectation maximization algorithm. Using posterior decoding, we observed two distinct shedding patterns: cows that had observations associated with a high-shedding disease state, and cows that did not. This model framework can be employed prospectively to determine which cows are likely to progress to clinical disease and may be applied to characterize disease progression of other slowly progressing infectious diseases.

scholarly journals An Efficient Algorithm for Estimating State Sequences in Imprecise Hidden Markov Models

2014 ◽  
Vol 50 ◽  
pp. 189-233 ◽  
Author(s):  
J. De Bock ◽  
G. De Cooman
Keyword(s):  
Hidden Markov Models ◽  
Character Recognition ◽  
Optical Character Recognition ◽  
Markov Models ◽  
Hidden Markov ◽  
Exact Algorithm ◽  
Mass Function ◽  
The State ◽  
Model Parameters ◽  
State Sequence

We present an efficient exact algorithm for estimating state sequences from outputs or observations in imprecise hidden Markov models (iHMMs). The uncertainty linking one state to the next, and that linking a state to its output, is represented by a set of probability mass functions instead of a single such mass function. We consider as best estimates for state sequences the maximal sequences for the posterior joint state model conditioned on the observed output sequence, associated with a gain function that is the indicator of the state sequence. This corresponds to and generalises finding the state sequence with the highest posterior probability in (precise-probabilistic) HMMs, thereby making our algorithm a generalisation of the one by Viterbi. We argue that the computational complexity of our algorithm is at worst quadratic in the length of the iHMM, cubic in the number of states, and essentially linear in the number of maximal state sequences. An important feature of our imprecise approach is that there may be more than one maximal sequence, typically in those instances where its precise-probabilistic counterpart is sensitive to the choice of prior. For binary iHMMs, we investigate experimentally how the number of maximal state sequences depends on the model parameters. We also present an application in optical character recognition, demonstrating that our algorithm can be usefully applied to robustify the inferences made by its precise-probabilistic counterpart.

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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