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Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
In this paper, we explore the class of the Hidden Semi-Markov Model (HSMM), a flexible extension of the popular Hidden Markov Model (HMM) that allows the underlying stochastic process to be a semi-Markov chain. HSMMs are typically used less…
The identification of factors associated with mental and behavioral disorders in early childhood is critical both for psychopathology research and the support of primary health care practices. Motivated by the Millennium Cohort Study, in…
When learning a hidden Markov model (HMM), sequen- tial observations can often be complemented by real-valued summary response variables generated from the path of hid- den states. Such settings arise in numerous domains, includ- ing many…
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
Markov decision processes are typically used for sequential decision making under uncertainty. For many aspects however, ranging from constrained or safe specifications to various kinds of temporal (non-Markovian) dependencies in task and…
For boundary-driven non-equilibrium Markov models of non-interacting particles in one dimension, either in continuous space with the Fokker-Planck dynamics involving an arbitrary force $F(x)$ and an arbitrary diffusion coefficient $D(x)$,…
Information seeking process is an important topic in information seeking behavior research. Both qualitative and empirical methods have been adopted in analyzing information seeking processes, with major focus on uncovering the latent…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow…
When clustering molecular dynamics (MD) trajectories into a few metastable conformational states, the Markov state models (MSMs) assumption of timescale separation between fast intrastate fluctuations and rarely occurring interstate…
We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\cdots M_1$, with the factors $M_i$ drawn independently…
Recommender systems help users find relevant items of interest based on the past preferences of those users. In many domains, however, the tastes and preferences of users change over time due to a variety of factors and recommender systems…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
Markov state models (MSMs) have been widely used to analyze computer simulations of various biomolecular systems. They can capture conformational transitions much slower than an average or maximal length of a single molecular dynamics (MD)…
Multivariate data sources with components of different information value seem to appear frequently in practice. Models in which the components change their homogeneity at different times are of significant importance. The fact whether any…