scholarly journals Recursive Deviance Information Criterion for the Hidden Markov Model

2015 ◽  
Vol 5 (1) ◽  
pp. 61
Author(s):  
Safaa K. Kadhem ◽  
Paul Hewson ◽  
Irene Kaimi
Keyword(s):  
Closed Form ◽  
Markov Models ◽  
Likelihood Function ◽  
Hidden Markov ◽  
Deviance Information Criterion ◽  
Synthetic Data ◽  
Information Criterion ◽  
Conditional Likelihood ◽  
Main Challenge ◽  
Hidden States

In Bayesian model selection, the deviance information criterion (DIC) has become a widely used criterion. It is however not defined for the hidden Markov models (HMMs). In particular, the main challenge of applying the DIC for HMMs is that the observed likelihood function of such models is not available in closed form. A closed form for the observed likelihood function can be obtained either by summing all possible hidden states of the complete likelihood using the so-called the forward recursion, or via integrating out the hidden states in the conditional likelihood. Hence, we propose two versions of the DIC to the model choice problem in HMMs context, namely, the recursive deviance-based DIC and the conditional likelihood-based DIC. In this paper, we compare several normal HMMs after they are estimated by Bayesian MCMC method. We conduct a simulation study based on synthetic data generated under two assumptions, namely diversity in the heterogeneity level and also the number of states. We show that the recursive deviance-based DIC performs well in selecting the correct model compared with the conditional likelihood-based DIC that prefers the more complicated models. A real application involving the waiting time of Old Faithful Geyser data was also used to check those criteria. All the simulations were conducted in Python v.2.7.10, available from first author on request.

An MEWMA-based segmental multivariate hidden Markov model for degradation assessment and prediction

2021 ◽  
pp. 1748006X2199052
Author(s):  
Yaping Li ◽  
Enrico Zio ◽  
Ershun Pan
Keyword(s):  
Markov Models ◽  
Hidden Markov ◽  
Average Run Length ◽  
Moving Average ◽  
Model Parameters ◽  
Current Time ◽  
Multivariate Processes ◽  
Industrial Systems ◽  
Hidden States ◽  
Multivariate Signals

Degradation is an unavoidable phenomenon in industrial systems. Hidden Markov models (HMMs) have been used for degradation modeling. In particular, segmental HMMs have been developed to model the explicit relationship between degradation signals and hidden states. However, existing segmental HMMs deal only with univariate cases, whereas in real systems, signals from various sensors are collected simultaneously, which makes it necessary to adapt the segmental HMMs to deal with multivariate processes. Also, to make full use of the information from the sensors, it is important to differentiate stable signals from deteriorating ones, but there is no good way for this, especially in multivariate processes. In this paper, the multivariate exponentially weighted moving average (MEWMA) control chart is employed to identify deteriorating multivariate signals. Specifically, the MEWMA statistic is used as a comprehensive indicator for differentiating multivariate observations. Likelihood Maximization is used to estimate the model parameters. To avoid underflow, the forward and backward probabilities are normalized. In order to assess degradation, joint probabilities are defined and derived. Further, the occurrence probability of each degradation state at the current time, as well as in the future, is derived. The Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset of NASA is employed for comparative analysis. In terms of degradation assessment and prediction, the proposed model performs very well in general. By sensitivity analysis, we show that in order to improve further the performance of the method, the weight of the chart should be set relatively small, whereas the method is not sensitive to the change of the in-control average run length (ARL).

scholarly journals Dynamic Transactions Between News Frames and Sociopolitical Events: An Integrative, Hidden Markov Model Approach

2020 ◽  
Vol 70 (3) ◽  
pp. 335-355 ◽  
Author(s):  
Frederic R Hopp ◽  
Jacob T Fisher ◽  
René Weber
Keyword(s):  
Markov Models ◽  
Hidden Markov ◽  
News Coverage ◽  
News Frames ◽  
Macro Scale ◽  
News Event ◽  
Hidden States ◽  
Research Domains ◽  
Integrated Study ◽  
Model Approach

Abstract A central goal of news research is to understand the interplay between news coverage and sociopolitical events. Although a great deal of work has elucidated how events drive news coverage, and how in turn news coverage influences societal outcomes, integrative systems-level models of the reciprocal interchanges between these two processes are sparse. Herein, we present a macro-scale investigation of the dynamic transactions between news frames and events using Hidden Markov Models (HMMs), focusing on morally charged news frames and sociopolitical events. Using 3,501,141 news records discussing 504,759 unique events, we demonstrate that sequences of frames and events can be characterized in terms of “hidden states” containing distinct moral frame and event relationships, and that these “hidden states” can forecast future news frames and events. This work serves to construct a path toward the integrated study of the news-event cycle across multiple research domains.

scholarly journals Use of Hidden Markov Models to Identify Background States Behind Risks of Cerebral Infarction and Ischemic Heart Disease

2017 ◽  
Vol 9 (1) ◽  
pp. 24
Author(s):  
Hiroshi Morimoto
Keyword(s):  
Heart Disease ◽  
Ischemic Heart Disease ◽  
Human Health ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Meteorological Factors ◽  
Hidden Markov ◽  
Weather Patterns ◽  
Weather And Human Health ◽  
Hidden States

Cold exposure is often said to trigger the incidence of cerebral infarctions and ischemic heart disease. This association between weather and human health has attracted considerable interest, and has been explored using standard statistical techniques such as regression models. Meteorological factors, such as temperature, are controlled by background systems, notably weather patterns. Therefore, it is reasonable to posit that the incidence of diseases is similarly influenced by a background system. The aim of this paper was to identify and construct these respective background systems. Possible background states or "hidden states", behind the incidence of diseases were derived using the EM and Viterbi algorithms with in the framework of hidden Markov models (HMM). A self-organizing map (SOM) enabled identification of weather patterns, considered as background states behind meteorological factors. These background states were then compared, and the hidden states behind the incidence of diseases were identified by six weather patterns. This finding indicates new evidence of the links between weather and human health, shedding light on the association between changes in the weather and the onset of disease. 

Extracting State Transition Dynamics from Multiple Spike Trains Using Hidden Markov Models with Correlated Poisson Distribution

2010 ◽  
Vol 22 (9) ◽  
pp. 2369-2389 ◽  
Author(s):  
Kentaro Katahira ◽  
Jun Nishikawa ◽  
Kazuo Okanoya ◽  
Masato Okada
Keyword(s):  
Hidden Markov Models ◽  
Poisson Distribution ◽  
State Transition ◽  
Markov Models ◽  
Hidden Markov ◽  
Synthetic Data ◽  
Poisson Model ◽  
Spike Trains ◽  
Output Distribution ◽  
Multivariate Poisson Distribution

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.

Extending hidden Markov models to allow conditioning on previous observations

2018 ◽  
Vol 16 (05) ◽  
pp. 1850019 ◽  
Author(s):  
Ioannis A. Tamposis ◽  
Margarita C. Theodoropoulou ◽  
Konstantinos D. Tsirigos ◽  
Pantelis G. Bagos
Keyword(s):  
Hidden Markov Models ◽  
Probabilistic Models ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Simple Extension ◽  
Computational Molecular Biology ◽  
Current State ◽  
Observation Sequence ◽  
Hidden States

Hidden Markov Models (HMMs) are probabilistic models widely used in computational molecular biology. However, the Markovian assumption regarding transition probabilities which dictates that the observed symbol depends only on the current state may not be sufficient for some biological problems. In order to overcome the limitations of the first order HMM, a number of extensions have been proposed in the literature to incorporate past information in HMMs conditioning either on the hidden states, or on the observations, or both. Here, we implement a simple extension of the standard HMM in which the current observed symbol (amino acid residue) depends both on the current state and on a series of observed previous symbols. The major advantage of the method is the simplicity in the implementation, which is achieved by properly transforming the observation sequence, using an extended alphabet. Thus, it can utilize all the available algorithms for the training and decoding of HMMs. We investigated the use of several encoding schemes and performed tests in a number of important biological problems previously studied by our team (prediction of transmembrane proteins and prediction of signal peptides). The evaluation shows that, when enough data are available, the performance increased by 1.8%–8.2% and the existing prediction methods may improve using this approach. The methods, for which the improvement was significant (PRED-TMBB2, PRED-TAT and HMM-TM), are available as web-servers freely accessible to academic users at www.compgen.org/tools/ .

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

Tensor Train Spectral Method for Learning of Hidden Markov Models (HMM)

2019 ◽  
Vol 19 (1) ◽  
pp. 93-99 ◽  
Author(s):  
Maxim A. Kuznetsov ◽  
Ivan V. Oseledets
Keyword(s):  
Probability Distribution ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Order Tensor ◽  
Spectral Learning ◽  
Frobenius Distance ◽  
Hidden States

AbstractWe propose a new algorithm for spectral learning of Hidden Markov Models (HMM). In contrast to the standard approach, we do not estimate the parameters of the HMM directly, but construct an estimate for the joint probability distribution. The idea is based on the representation of a joint probability distribution as an N-th-order tensor with low ranks represented in the tensor train (TT) format. Using TT-format, we get an approximation by minimizing the Frobenius distance between the empirical joint probability distribution and tensors with low TT-ranks with core tensors normalization constraints. We propose an algorithm for the solution of the optimization problem that is based on the alternating least squares (ALS) approach and develop its fast version for sparse tensors. The order of the tensor d is a parameter of our algorithm. We have compared the performance of our algorithm with the existing algorithm by Hsu, Kakade and Zhang proposed in 2009 and found that it is much more robust if the number of hidden states is overestimated.

scholarly journals Classifying Eye Movement Events With an Unsupervised Generative Hidden Markov Model

2020 ◽  
Author(s):  
Malte Lüken ◽  
Šimon Kucharský ◽  
Ingmar Visser
Keyword(s):  
Eye Movement ◽  
Markov Models ◽  
Hidden Markov ◽  
Simulated Data ◽  
Generative Models ◽  
Critical Parameters ◽  
Small Noise ◽  
Dynamic Stimuli ◽  
Benchmark Data ◽  
Hidden States

Eye-tracking allows researchers to infer cognitive processes from eye movements that are classified into distinct events. Parsing the events is typically done by algorithms. Previous algorithms have successfully used hidden Markov models (HMMs) for classification but can still be improved in several aspects. To address these aspects, we developed gazeHMM, an algorithm that uses an HMM as a generative model, has no critical parameters to be set by users, and does not require human coded data as input. The algorithm classifies gaze data into fixations, saccades, and optionally postsaccadic oscillations and smooth pursuits. We evaluated gazeHMM’s performance in a simulation study, showing that it successfully recovered HMM parameters and hidden states. Parameters were less well recovered when we included a smooth pursuit state and/or added even small noise to simulated data. We applied generative models with different numbers of events to benchmark data. Comparing them indicated that HMMs with more events than expected had most likely generated the data. We also applied the full algorithm to benchmark data and assessed its similarity to human coding. For static stimuli, gazeHMM showed high similarity and outperformed other algorithms in this regard. For dynamic stimuli, gazeHMM tended to rapidly switch between fixations and smooth pursuits but still displayed higher similarity than other algorithms. Concluding that gazeHMM can be used in practice, we recommend parsing smooth pursuits only for exploratory purposes. Future HMM algorithms could use covariates to better capture eye movement processes and explicitly model event durations to classify smooth pursuits more accurately.

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