Bayesian Hidden Markov Model Research Articles

DBHC: Discrete Bayesian HMM Clustering

Sequence data mining has become an increasingly popular research topic as the availability of data has grown rapidly over the past decades. Sequence clustering is a type of method within this field that is in high demand in the industry, but the sequence clustering problem is non-trivial and, as opposed to static cluster analysis, interpreting clusters of sequences is often difficult. Using Hidden Markov Models (HMMs), we propose the Discrete Bayesian HMM Clustering (DBHC) algorithm, an approach to clustering discrete sequences by extending a proven method for continuous sequences. The proposed algorithm is completely self-contained as it incorporates both the search for the number of clusters and the search for the number of hidden states in each cluster model in the parameter inference. We provide a working example and a simulation study to explain and showcase the capabilities of the DBHC algorithm. A case study illustrates how the hidden states in a mixture of HMMs can aid the interpretation task of a sequence cluster analysis. We conclude that the algorithm works well as it provides well-interpretable clusters for the considered application.

Bayesian multilevel hidden Markov models identify stable state dynamics in longitudinal recordings from macaque primary motor cortex.

Neural populations, rather than single neurons, may be the fundamental unit of cortical computation. Analysing chronically recorded neural population activity is challenging not only because of the high dimensionality of activity but also because of changes in the signal that may or may not be due to neural plasticity. Hidden Markov models (HMMs) are a promising technique for analysing such data in terms of discrete latent states, but previous approaches have not considered the statistical properties of neural spiking data, have not been adaptable to longitudinal data, or have not modelled condition-specific differences. We present a multilevel Bayesian HMM addresses these shortcomings by incorporating multivariate Poisson log-normal emission probability distributions, multilevel parameter estimation and trial-specific condition covariates. We applied this framework to multi-unit neural spiking data recorded using chronically implanted multi-electrode arrays from macaque primary motor cortex during a cued reaching, grasping and placing task. We show that, in line with previous work, the model identifies latent neural population states which are tightly linked to behavioural events, despite the model being trained without any information about event timing. The association between these states and corresponding behaviour is consistent across multiple days of recording. Notably, this consistency is not observed in the case of a single-level HMM, which fails to generalise across distinct recording sessions. The utility and stability of this approach is demonstrated using a previously learned task, but this multilevel Bayesian HMM framework would be especially suited for future studies of long-term plasticity in neural populations.

Inferring longitudinal patterns of group B Streptococcus colonization during pregnancy

Maternal colonization by Group B Streptococcus (GBS) can lead to severe infection in neonates and has also been associated with prematurity and stillbirth. Better quantitative understanding of the trajectories of GBS carriage during pregnancy is essential for the design of informative epidemiological studies. Here, we describe analyses of published longitudinal data using Bayesian hidden Markov models, which involve the estimation of parameters related to the succession of latent states (infection status) and observations (culture positivity). In addition to quantifying infection acquisition and clearance probabilities, the statistical approach also suggests that for some longitudinal patterns of culture results, pregnant women were likely to have been GBS-colonized despite a negative diagnostic result. We believe this method, if used in future longitudinal studies of maternal GBS colonization, would improve our understanding of the pathologies linked to this bacterium and could also inform maternal GBS vaccine trial design.

Compressed computations using wavelets for hidden Markov models with continuous observations.

Compression as an accelerant of computation is increasingly recognized as an important component in engineering fast real-world machine learning methods for big data; c.f., its impact on genome-scale approximate string matching. Previous work showed that compression can accelerate algorithms for Hidden Markov Models (HMM) with discrete observations, both for the classical frequentist HMM algorithms-Forward Filtering, Backward Smoothing and Viterbi-and Gibbs sampling for Bayesian HMM. For Bayesian HMM with continuous-valued observations, compression was shown to greatly accelerate computations for specific types of data. For instance, data from large-scale experiments interrogating structural genetic variation can be assumed to be piece-wise constant with noise, or, equivalently, data generated by HMM with dominant self-transition probabilities. Here we extend the compressive computation approach to the classical frequentist HMM algorithms on continuous-valued observations, providing the first compressive approach for this problem. In a large-scale simulation study, we demonstrate empirically that in many settings compressed HMM algorithms very clearly outperform the classical algorithms with no, or only an insignificant effect, on the computed probabilities and infered state paths of maximal likelihood. This provides an efficient approach to big data computations with HMM. An open-source implementation of the method is available from https://github.com/lucabello/wavelet-hmms.

A framework for assessing confidence in freedom from infection in animal disease control programmes.

In the Surveillance Tool for Outcome-based Comparison of FREEdom from infection (STOC free) project (https://www.stocfree.eu), a data collection tool was constructed to facilitate standardised collection of input data, and a model was developed to allow a standardised and harmonised comparison of the outputs of different control programmes (CPs) for cattle diseases. The STOC free model can be used to evaluate the probability of freedom from infection for herds in CPs and to determine whether these CPs comply with the European Union's pre-defined output-based standards. Bovine viral diarrhoea virus (BVDV) was chosen as the case disease for this project because of the diversity in CPs in the six participating countries. Detailed BVDV CP and risk factor information was collected using the data collection tool. For inclusion of the data in the STOC free model, key aspects and default values were quantified. A Bayesian hidden Markov model was deemed appropriate, and a model was developed for BVDV CPs. The model was tested and validated using real BVDV CP data from partner countries, and corresponding computer code was made publicly available. The STOC free model focuses on herd-level data, although that animal-level data can be included after aggregation to herd level. The STOC free model is applicable to diseases that are endemic, given that it needs the presence of some infection to estimate parameters and enable convergence. In countries where infection-free status has been achieved, a scenario tree model could be a better suited tool. Further work is recommended to generalise the STOC free model to other diseases.

Comparison of the confidence in freedom from infection based on different control programmes between EU member states: STOC free

The STOC free project constructed a generic framework that allows a standardised and harmonised description of different control programmes (CP) for cattle diseases. The STOC free model can be used to determine the confidence of freedom from infection that has been achieved in disease CPs, in support of an ongoing assessment of progress towards output-based standards as outlined in the EU Animal Health Law. With this information, and as required, further CP actions can be taken to mitigate the risks of persistence and (re-)introduction on the probability of freedom from infection. Bovine viral diarrhoea virus (BVDV) was chosen as the case disease because of the diversity in CPs in the six participating countries. A Bayesian hidden Markov model was considered the best modelling method. Detailed BVDV CP information was collected in the participating countries and the key aspects for inclusion in the STOC free model were identified. A first version of STOC free model was developed and tested on simulated data. The risk factors for BVDV infection that needed to be included in the model were defined and default values for these risk factors were quantified. A data collection tool was finalised with which the data for the STOC free model was collected. Subsequently, the developed model was tested and validated using real BVDV CP data from partner countries. Based on the feedback, the model was finalised and the report and corresponding computer code were made publicly available. There were roughly three different BVDV situations that occurred in the partner countries: 1. Endemic situation with a CP operating at herd level, 2. Endemic situation with a CP operating at animal level and 3. BVD free situation. The STOC free model is able to include herd level data only and animal level data has to be aggregated to herd level before the model can be applied. The STOC free model is not applicable for a country that is completely BVDV free given that it needs some infections to estimate its parameters and converge. In the latter situation, a scenario tree model could be a better suited tool, and this was evaluated in the Swedish case study. Further work is needed for generalisation of the method to other diseases and expansion of the method to include socioeconomic aspects of CPs.

Scalable Inference for Hybrid Bayesian Hidden Markov Model Using Gaussian Process Emission

The hidden Markov model (HMM), used with Gaussian Process (GP) as an emission model, has been widely used to model sequential data in complex form. This study introduces the hybrid Bayesian HMM with GP emission using SM kernel (HMM-GPSM) to estimate the hidden state of each time-series observation, that is, sequentially observed from a single channel. We then propose a scalable inference method to train the HMM-GPSM using large-scale sequences of time-series dataset that has (1) a large number of sequences for state transitions and (2) a large number of data points in a time-series observation for each hidden state. For state transitions with a large number of sequences, we employ stochastic variational inference (SVI) to update the parameters of HMM-GPSM efficiently. Also, for each time-series observation that has a large number of data points, we propose the approximate GP emission using the Random Fourier Feature (RFF), which is constructed by using the spectral points that are sampled from the spectral density of SM kernel. We propose the efficient inference of the kernel hyperparameters of the approximate GP emission and corresponding HMM-GPSM. Specifically, we derive the training loss, that is, the evidence lower bound of the HMM-GPSM that can be scalably computed for a large number of time-series observations by employing the regularized lower bound of GP emission likelihood with KL divergence. The proposed methods can be used together to train HMM-GPSM with the sequential time-series dataset that contains both (1) and (2). We validate the proposed method on the synthetic and real datasets using the clustering accuracy, marginal likelihood, and training time as the performance metrics.

Exploring the predictability of cryptocurrencies via Bayesian hidden Markov models

In this paper, we consider a variety of multi-state hidden Markov models for predicting and explaining the Bitcoin, Ether and Ripple returns in the presence of state (regime) dynamics. In addition, we examine the effects of several financial, economic and cryptocurrency specific predictors on the cryptocurrency return series. Our results indicate that the non-homogeneous hidden Markov (NHHM) model with four states has the best one-step-ahead forecasting performance among all competing models for all three series. The dominance of the predictive densities over the single regime random walk model relies on the fact that the states capture alternating periods with distinct return characteristics. In particular, the four state NHHM model distinguishes bull, bear and calm regimes for the Bitcoin series, and periods with different profit and risk magnitudes for the Ether and Ripple series. Also, conditionally on the hidden states, it identifies predictors with different linear and non-linear effects on the cryptocurrency returns. These empirical findings provide important benefits for portfolio management and policy implementation.

MAP segmentation in Bayesian hidden Markov models: a case study

We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have Dirichlet priors. We study a training set consisting of thousands of protein alignment pairs. The training data is used to set the prior hyperparameters for Bayesian MAP segmentation. Since the Viterbi algorithm is not applicable any more, there is no simple procedure to find the MAP path, and several iterative algorithms are considered and compared. The main goal of the paper is to test the Bayesian setup against the frequentist one, where the parameters of HMM are estimated using the training data.

Social Visual Perception Under the Eye of Bayesian Theories in Autism Spectrum Disorder Using Advanced Modeling of Spatial and Temporal Parameters.

Social interaction in individuals with Autism Spectrum Disorder (ASD) is characterized by qualitative impairments that highly impact quality of life. Bayesian theories in ASD frame an understanding of underlying mechanisms suggesting atypicalities in the evaluation of probabilistic links within the perceptual environment of the affected individual. To address these theories, the present study explores the applicability of an innovative Bayesian framework on social visual perception in ASD and demonstrates the use of gaze transitions between different parts of social scenes. We applied advanced analyses with Bayesian Hidden Markov Modeling (BHMM) to track gaze movements while presenting real-life scenes to typically developing (TD) children and adolescents (N = 25) and participants with ASD and Attention-Deficit/Hyperactivity Disorder (ASD+ADHD, N = 15) and ASD without comorbidity (ASD, N = 12). Regions of interest (ROIs) were generated by BHMM based both on spatial and temporal gaze behavior. Social visual perception was compared between groups using transition and fixation variables for social (faces, bodies) and non-social ROIs. Transition variables between faces, namely gaze transitions between faces and likelihood of linking faces, were reduced in the ASD+ADHD compared to TD participants. Fixation count to faces was also reduced in this group. The ASD group showed similar performance to TD in the studied variables. There was no difference between groups for non-social ROIs. Our study provides an innovative, interpretable example of applying Bayesian theories of social visual perception in ASD. BHMM analyses and gaze transitions have the potential to reveal fundamental social perception components in ASD, contributing thus to amelioration of social-skill interventions.

A New Method to Reconstruct Quantitative Food Webs and Nutrient Flows from Isotope Tracer Addition Experiments.

Understanding how nutrients flow through food webs is central in ecosystem ecology. Tracer addition experiments are powerful tools to reconstruct nutrient flows by adding an isotopically enriched element into an ecosystem and tracking its fate through time. Historically, the design and analysis of tracer studies have varied widely, ranging from descriptive studies to modeling approaches of varying complexity. Increasingly, isotope tracer data are being used to compare ecosystems and analyze experimental manipulations. Currently, a formal statistical framework for analyzing such experiments is lacking, making it impossible to calculate the estimation errors associated with the model fit, the interdependence of compartments, and the uncertainty in the diet of consumers. In this article we develop a method based on Bayesian hidden Markov models and apply it to the analysis of tracer additions in two Trinidadian streams in which light was experimentally manipulated. Through this case study, we illustrate how to estimate N fluxes between ecosystem compartments, turnover rates of N within those compartments, and the associated uncertainty. We also show how the method can be used to compare alternative models of food web structure, calculate the error around derived parameters, and make statistical comparisons between sites or treatments.

Hidden Markov model in multiple testing on dependent count data

ABSTRACTMultiple testing on dependent count data faces two basic modelling elements: the choice of distributions under the null and the non-null states and the modelling of the dependence structure across observations. A Bayesian hidden Markov model is constructed for Poisson count data to handle these two issues. The proposed Bayesian method is based on the posterior probability of the null state and exhibits the property of an optimal test procedure, which has the lowest false-negative rate with the false discovery rate under control. Furthermore, the model has either single or mixture of Poisson distributions used under the non-null state. Model selection methods are employed here to decide the number of components in the mixture. Different approaches of calculating marginal likelihood are discussed. Extensive simulation studies and a case study are employed to examine and compare a collection of commonly used testing procedures and model selection criteria.

Analysis of Speaker Diarization Based on Bayesian HMM With Eigenvoice Priors

In our previous work, we introduced our Bayesian Hidden Markov Model with eigenvoice priors, which has been recently recognized as the state-of-the-art model for Speaker Diarization. In this article we present a more complete analysis of the Diarization system. The inference of the model is fully described and derivations of all update formulas are provided for a complete understanding of the algorithm. An extensive analysis on the effect, sensitivity and interactions of all model parameters is provided, which might be used as a guide for their optimal setting. The newly introduced speaker regularization coefficient allows us to control the number of speakers inferred in an utterance. A naive speaker model merging strategy is also presented, which allows to drive the variational inference out of local optima. Experiments for the different diarization scenarios are presented on CALLHOME and DIHARD datasets.

Integrated Cognitive Architecture for Robot Learning of Action and Language.

The manner in which humans learn, plan, and decide actions is a very compelling subject. Moreover, the mechanism behind high-level cognitive functions, such as action planning, language understanding, and logical thinking, has not yet been fully implemented in robotics. In this paper, we propose a framework for the simultaneously comprehension of concepts, actions, and language as a first step toward this goal. This can be achieved by integrating various cognitive modules and leveraging mainly multimodal categorization by using multilayered multimodal latent Dirichlet allocation (mMLDA). The integration of reinforcement learning and mMLDA enables actions based on understanding. Furthermore, the mMLDA, in conjunction with grammar learning and based on the Bayesian hidden Markov model (BHMM), allows the robot to verbalize its own actions and understand user utterances. We verify the potential of the proposed architecture through experiments using a real robot.

Estimation of Viterbi path in Bayesian hidden Markov models

The article studies different methods for estimating the Viterbi path in the Bayesian framework. The Viterbi path is an estimate of the underlying state path in hidden Markov models (HMMs), which has a maximum joint posterior probability. Hence it is also called the maximum a posteriori (MAP) path. For an HMM with given parameters, the Viterbi path can be easily found with the Viterbi algorithm. In the Bayesian framework the Viterbi algorithm is not applicable and several iterative methods can be used instead. We introduce a new EM-type algorithm for finding the MAP path and compare it with various other methods for finding the MAP path, including the variational Bayes approach and MCMC methods. Examples with simulated data are used to compare the performance of the methods. The main focus is on non-stochastic iterative methods and our results show that the best of those methods work as well or better than the best MCMC methods. Our results demonstrate that when the primary goal is segmentation, then it is more reasonable to perform segmentation directly by considering the transition and emission parameters as nuisance parameters.

Understanding Human Action using a Bayesian HMM with a Continuous Gaussian-Wishart Emission Model

Understanding human action has become a popular issue in artificial intelligence. To address this, we propose combining a Bayesian hidden Markov model (HMM) with a continuous Gaussian-Wishart emission model. First, we define the HMM with the Gaussian-Wishart emission mixture model to express a sequence of continuous observation feature vectors from a human action video. Second, we use an approximated variational Bayesian inference to derive posterior distributions for hidden variables and parameters required to define the proposed model. Third, we derive the approximated predictive distribution for an observation sequence that can be used to represent a new action, and then, we compute a likelihood function that indicates the probability that the new observation sequence belongs to each class using the approximated predictive distribution. Fourth, we classify the new action into a human action category that maximizes the likelihood function value. Finally, to evaluate the performance of the proposed method, we conduct human action classification using a KTH human action dataset. The experimental results show that the recognition rate with our method is in the middle position among various existing methods.

A Sequential Approach to Market State Modeling and Analysis in Online P2P Lending

Online peer-to-peer (P2P) lending is an emerging wealth-management service for individuals, which allows lenders to directly bid and invest on the listings created by borrowers without going through any traditional financial intermediaries. As a nonbank financial platform, online P2P lending tends to have both high volatility and liquidity. Therefore, it is of significant importance to discern the hidden market states of the listings (e.g., hot and cold), which open venues for enhancing business analytics and investment decision making. However, the problem of market state modeling remains pretty open due to many technical and domain challenges, such as the dynamic and sequential characteristics of listings. To that end, in this paper, we present a focused study on market state modeling and analysis for online P2P lending. Specifically, we first propose two enhanced sequential models by extending the Bayesian hidden Markov model (BHMM), namely listing-BHMM (L-BHMM) and listing and marketing-BHMM (LM-BHMM), for learning the latent semantics between listings’ market states and lenders’ bidding behaviors. Particularly, L-BHMM is a straightforward model that only considers the local observations of a listing itself, while LM-BHMM considers not only the listing information but also the global information of current market (e.g., the competitive and complementary relations among listings). Furthermore, we demonstrate several motivating applications enabled by our models, such as bidding prediction and herding detection. Finally, we construct extensive experiments on two real-world data sets and make some deep analysis on bidding behaviors, which clearly validate the effectiveness of our models in terms of different applications and also reveal some interesting business findings.

Using HaMMLET for Bayesian Segmentation of WGS Read-Depth Data.

CNV detection requires a high-quality segmentation of genomic data. In many WGS experiments, sample and control are sequenced together in a multiplexed fashion using DNA barcoding for economic reasons. Using the differential read depth of these two conditions cancels out systematic additive errors. Due to this detrending, the resulting data is appropriate for inference using a hidden Markov model (HMM), arguably one of the principal models for labeled segmentation. However, while the usual frequentist approaches such as Baum-Welch are problematic for several reasons, they are often preferred to Bayesian HMM inference, which normally requires prohibitively long running times and exceeds a typical user's computational resources on a genome scale data. HaMMLET solves this problem using a dynamic wavelet compression scheme, which makes Bayesian segmentation of WGS data feasible on standard consumer hardware.

Machine Learning Based Big Data Processing Framework for Cancer Diagnosis Using Hidden Markov Model and GM Clustering

The change in the DNA is a form of genetic variation in the human genome. In addition, the DNA copy number change is also linked with the progression of many emerging diseases. Array-based Comparative Genomic Hybridization (CGH) is considered as a major task when measuring the DNA copy number change across the genome. Moreover, DNA copy number change is an essential measure to diagnose the cancer disease. Next generation sequencing is an important method for studying the spread of infectious disease qualitatively and quantitatively. CGH is widely used in continuous monitoring of copy number of thousands of genes throughout the genome. In recent years, the size of the DNA sequence data is very large. Hence, there is a need to use a scalable machine learning approach to overcome the various issues in DNA copy number change detection. In this paper, we use a Bayesian hidden Markov model (HMM) with Gaussian Mixture (GM) Clustering approach to model the DNA copy number change across the genome. The proposed Bayesian HMM with GM Clustering approach is compared with various existing approaches such as Pruned Exact Linear Time method, binary segmentation method and segment neighborhood method. Experimental results demonstrate the effectiveness of our proposed change detection algorithm.

Bayesian hidden Markov models in DNA sequence segmentation using R: the case of Simian Vacuolating virus (SV40)

ABSTRACTSegmentation models aim to partition compositionally heterogeneous domains into homogeneous segments which may be reflective of biological function. Due to the latent nature of the segments a natural approach to segmentation that has gained favour recently uses Bayesian hidden Markov models (HMMs). Concomitantly in the last few decades, the free R programming language has become a dominant tool for computational statistics, visualization and data science. Therefore, this paper aims to fully exploit R to fit a Bayesian HMM for DNA segmentation. The joint posterior distribution of parameters in the model to be considered is derived followed by the algorithms that can be used for estimation. Functions following these algorithms (Gibbs Sampling, Data Augmentation and Label Switching) are then fully implemented in R. The methodology is assessed through extensive simulation studies and then being applied to analyse Simian Vacuolating virus (SV40). It is concluded that: (1) the algorithms and functions in R can correctly estimate sequence segmentation if the HMM structure is assumed; (2) the performance of the model improves with sequence length; (3) R is reasonably fast for short to medium sequence lengths and number of segments and (4) the segmentation of SV40 appears to correspond with the two major transcripts, early and late, that regulate the expression of SV40 genes.