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We present an efficient exact algorithm for estimating state sequences from outputs (or observations) in imprecise hidden Markov models (iHMM), where both the uncertainty linking one state to the next, and that linking a state to its…
Profile hidden Markov models (pHMMs) are widely employed in various bioinformatics applications to identify similarities between biological sequences, such as DNA or protein sequences. In pHMMs, sequences are represented as graph…
We propose a new constrained EM algorithm that is applicable to general constrained estimation problems. The proposed method is based on a novel framework, the `dual-homotopy framework,' which combines deterministic annealing EM with a…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the…
As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We…
Hidden Markov models (HMM) are commonly used in generation tasks and have demonstrated strong capabilities in neuro-symbolic applications for the Markov property. These applications leverage the strengths of neural networks and symbolic…
This paper addresses the issue of model selection for hidden Markov models (HMMs). We generalize factorized asymptotic Bayesian inference (FAB), which has been recently developed for model selection on independent hidden variables (i.e.,…
To avoid specification of the error distribution in a regression model, we propose a general nonparametric scale mixture model for the error distribution. For fitting such mixtures, the predictive recursion method is a simple and…
The formalism of state estimation and hidden Markov models (HMMs) can simplify and clarify the discussion of stochastic thermodynamics in the presence of feedback and measurement errors. After reviewing the basic formalism, we use it to…
We propose a hidden Markov model for univariate proportion time series taking values in (0,1), where regime switching captures latent structural changes and the emission distribution belongs to the Beta family. In each latent state, the…
A non linear regression approach which consists of a specific regression model incorporating a latent process, allowing various polynomial regression models to be activated preferentially and smoothly, is introduced in this paper. The model…
This paper presents a mathematical framework for causal nonlinear prediction in settings where observations are generated from an underlying hidden Markov model (HMM). Both the problem formulation and the proposed solution are motivated by…
In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…
The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we…
Stochastic volatility models are the backbone of financial engineering. We study both continuous time diffusions as well as discrete time models. We propose two novel approaches to estimating stochastic volatility diffusions, one using…
We consider the smoothing probabilities of hidden Markov model (HMM). We show that under fairly general conditions for HMM, the exponential forgetting still holds, and the smoothing probabilities can be well approximated with the ones of…
Pair Hidden Markov Models (PHMMs) are probabilistic models used for pairwise sequence alignment, a quintessential problem in bioinformatics. PHMMs include three types of hidden states: match, insertion and deletion. Most previous studies…
Analysis of multivariate healthcare time series data is inherently challenging: irregular sampling, noisy and missing values, and heterogeneous patient groups with different dynamics violating exchangeability. In addition, interpretability…
Hidden Markov models provide a natural statistical framework for the detection of the copy number variations (CNV) in genomics. In this paper, we consider a Hidden Markov Model involving several correlated hidden processes at the same time.…