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We present a new algorithm for identifying the transition and emission probabilities of a hidden Markov model (HMM) from the emitted data. Expectation-maximization becomes computationally prohibitive for long observation records, which are…

Social learning strategies enable agents to infer the underlying true state of nature in a distributed manner by receiving private environmental signals and exchanging beliefs with their neighbors. Previous studies have extensively focused…

While continuous diffusion models excel in modeling continuous distributions, their application to categorical data has been less effective. Recent work has shown that ratio-matching through score-entropy within a continuous-time discrete…

Biological systems need to react to stimuli over a broad spectrum of timescales. If and how this ability can emerge without external fine-tuning is a puzzle. We consider here this problem in discrete Markovian systems, where we can leverage…

Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…

We describe a generalization of the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) which is able to encode prior information that state transitions are more likely between "nearby" states. This is accomplished by defining a…

We investigate a novel modeling approach for end-to-end neural network training using hidden Markov models (HMM) where the transition probabilities between hidden states are modeled and learned explicitly. Most contemporary…

Many works have been proposed in the literature to capture the dynamics of diffusion in networks. While some of them define graphical markovian models to extract temporal relationships between node infections in networks, others consider…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

Suppose that we are given a time series where consecutive samples are believed to come from a probabilistic source, that the source changes from time to time and that the total number of sources is fixed. Our objective is to estimate the…

This paper is concerned with the computational complexity of learning the Hidden Markov Model (HMM). Although HMMs are some of the most widely used tools in sequential and time series modeling, they are cryptographically hard to learn in…

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…

We present a general framework for applying learning algorithms and heuristical guidance to the verification of Markov decision processes (MDPs). The primary goal of our techniques is to improve performance by avoiding an exhaustive…

These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…

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…

In this paper we consider a reduced-form intensity-based credit risk model with a hidden Markov state process. A filtering method is proposed for extracting the underlying state given the observation processes. The method may be applied to…

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…

We study the frontier between learnable and unlearnable hidden Markov models (HMMs). HMMs are flexible tools for clustering dependent data coming from unknown populations. The model parameters are known to be fully identifiable (up to…

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…

Hidden Markov models (HMMs) are flexible tools for clustering dependent data coming from unknown populations, allowing nonparametric modelling of the population densities. Identifiability fails when the data is in fact independent and…