Related papers: Estimation and selection for high-order Markov cha…

We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…

We consider a class of colored graphical Gaussian models obtained by placing symmetry constraints on the precision matrix in a Bayesian framework. The prior distribution on the precision matrix is the colored $G$-Wishart prior which is the…

Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…

In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of…

We propose a new Markov chain Monte Carlo method in which trial configurations are generated by evolving a state, sampled from a prior distribution, using a Markov transition matrix. We present two prototypical algorithms and derive their…

Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for…

Bayesian mixture models are widely applied for unsupervised learning and exploratory data analysis. Markov chain Monte Carlo based on Gibbs sampling and split-merge moves are widely used for inference in these models. However, both methods…

The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behavior. In this paper, for a higher order Markov chain, we establish some properties related to its exact limiting…

Predictive constructions are a powerful way of characterizing the probability law of stochastic processes with certain forms of invariance, such as exchangeability or Markov exchangeability. When de Finetti-like representation theorems are…

We determine an explicit Gr\"obner basis, consisting of linear forms and determinantal quadrics, for the prime ideal of Raftery's mixture transition distribution model for Markov chains. When the states are binary, the corresponding…

We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given…

There is a growing interest in learning how the distribution of a response variable changes with a set of predictors. Bayesian nonparametric dependent mixture models provide a flexible approach to address this goal. However, several…

Models for categorical sequences typically assume exchangeable or first-order dependent sequence elements. These are common assumptions, for example, in models of computer malware traces and protein sequences. Although such simplifying…

In this work we introduce a new and richer class of finite order Markov chain models and address the following model selection problem: find the Markov model with the minimal set of parameters (minimal Markov model) which is necessary to…

Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…

We propose a probabilistic modeling framework for learning the dynamic patterns in the collective behaviors of social agents and developing profiles for different behavioral groups, using data collected from multiple information sources.…

Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…

Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…