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Admixture models are a ubiquitous approach to capture latent population structure in genetic samples. Despite the widespread application of admixture models, little thought has been devoted to the quality of the model fit or the accuracy of…

Model ensembling is a well-established technique for improving the performance of machine learning models. Conventionally, this involves averaging the output distributions of multiple models and selecting the most probable label. This idea…

De-interleaving of the mixtures of Hidden Markov Processes (HMPs) generally depends on its representation model. Existing representation models consider Markov chain mixtures rather than hidden Markov, resulting in the lack of robustness to…

Under Markovian assumptions, we leverage a Central Limit Theorem (CLT) for the empirical measure in the test statistic of the composite hypothesis Hoeffding test so as to establish weak convergence results for the test statistic, and,…

Network data is prevalent in many contemporary big data applications in which a common interest is to unveil important latent links between different pairs of nodes. Yet a simple fundamental question of how to precisely quantify the…

A hidden Markov model with trends is a hidden Markov model whose emission distributions are translated by a trend that depends on the current hidden state and on the current time. Contrary to standard hidden Markov models, such processes…

Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…

In the genomic era, the identification of gene signatures associated with disease is of significant interest. Such signatures are often used to predict clinical outcomes in new patients and aid clinical decision-making. However, recent…

Likelihood-free inference methods based on neural conditional density estimation were shown to drastically reduce the simulation burden in comparison to classical methods such as ABC. When applied in the context of any latent variable…

Hidden Markov model (HMM) has been successfully used for sequential data modeling problems. In this work, we propose to power the modeling capacity of HMM by bringing in neural network based generative models. The proposed model is termed…

We develop a stochastic epidemic model progressing over dynamic networks, where infection rates are heterogeneous and may vary with individual-level covariates. The joint dynamics are modeled as a continuous-time Markov chain such that…

Hidden Markov models (HMM) have been widely used by scientists to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of…

Model selection, via penalized likelihood type criteria, is a standard task in many statistical inference and machine learning problems. Progress has led to deriving criteria with asymptotic consistency results and an increasing emphasis on…

Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is…

In applications such as gene regulatory network analysis based on single-cell RNA sequencing data, samples often come from a mixture of different populations and each population has its own unique network. Available graphical models often…

A hidden Markov model (HMM) is said to have path-mergeable states if for any two states i,j there exists a word w and state k such that it is possible to transition from both i and j to k while emitting w. We show that for a finite HMM with…

A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we show how HMMs can be extended with side-constraints and present…

Admixed populations are formed by the merging of two or more ancestral populations, and the ancestry of each locus in an admixed genome derives from either source. Consider a simple "pulse" admixture model, where populations A and B merged…

While linear mixed model (LMM) has shown a competitive performance in correcting spurious associations raised by population stratification, family structures, and cryptic relatedness, more challenges are still to be addressed regarding the…

Hidden Markov Models (HMMs) are a commonly used tool for inference of transcription factor (TF) binding sites from DNA sequence data. We exploit the mathematical equivalence between HMMs for TF binding and the "inverse" statistical…