Related papers: Modelling Large Dimensional Datasets with Markov S…

In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the…

Estimating hidden states in dynamical systems, also known as optimal filtering, is a long-standing problem in various fields of science and engineering. In this paper, we introduce a general filtering framework, \textbf{LLM-Filter}, which…

We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…

Motivated by applications arising in networked systems, this work examines controlled regime-switching systems that stem from a mean-variance formulation. A main point is that the switching process is a hidden Markov chain. An additional…

Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle…

Forecasting tasks using large datasets gathering thousands of heterogeneous time series is a crucial statistical problem in numerous sectors. The main challenge is to model a rich variety of time series, leverage any available external…

We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…

Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p x p covariance matrix into the sum of two components. Through a latent factor representation, they can…

Time series subject to change in regime have attracted much interest in domains such as econometry, finance or meteorology. For discrete-valued regimes, some models such as the popular Hidden Markov Chain (HMC) describe time series whose…

Hidden Markov Models (HMM) model a sequence of observations that are dependent on a hidden (or latent) state that follow a Markov chain. These models are widely used in diverse fields including ecology, speech recognition, and…

High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix…

We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show…

This work proposes a multi-agent filtering algorithm over graphs for finite-state hidden Markov models (HMMs), which can be used for sequential state estimation or for tracking opinion formation over dynamic social networks. We show that…

Bayes factor, defined as the ratio of the marginal likelihood functions of two competing models, is the natural Bayesian procedure for model selection. Marginal likelihoods are usually computationally demanding and complex. This scenario is…

Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…

We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or…

We illustrate a class of conditional models for the analysis of longitudinal data suffering attrition in random effects models framework, where the subject-specific random effects are assumed to be discrete and to follow a time-dependent…

This article introduces a nonlinear generalized matrix factor model (GMFM) that allows for mixed-type variables, extending the scope of linear matrix factor models (LMFM) that are so far limited to handling continuous variables. We…

Non-homogeneous hidden Markov models (NHHMM) are a subclass of dependent mixture models used for semi-supervised learning, where both transition probabilities between the latent states and mean parameter of the probability distribution of…

Large Language Models (LLMs) are reshaping the research landscape in artificial intelligence, particularly as model parameters scale up significantly, unlocking remarkable capabilities across various domains. Nevertheless, the scalability…