Related papers: Piecewise deterministic generative models
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
The Bouncy Particle sampler (BPS) and the Zig-Zag sampler (ZZS) are continuous time, non-reversible Monte Carlo methods based on piecewise deterministic Markov processes. Experiments show that the speed of convergence of these samplers can…
We extend the hypocoercivity framework for piecewise-deterministic Markov process (PDMP) Monte Carlo established in [Andrieu et. al. (2018)] to heavy-tailed target distributions, which exhibit subgeometric rates of convergence to…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
Neural Temporal Point Processes (TPPs) have emerged as the primary framework for predicting sequences of events that occur at irregular time intervals, but their sequential nature can hamper performance for long-horizon forecasts. To…
Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models,…
We propose a deterministic denoising algorithm for discrete-state diffusion models. The key idea is to derandomize the generative reverse Markov chain by introducing a variant of the herding algorithm, which induces deterministic state…
Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging…
Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…
Control theory plays a pivotal role in understanding and optimizing the behavior of complex dynamical systems across various scientific and engineering disciplines. Two key frameworks that have emerged for modeling and solving control…
Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the underlying process impacts both algorithmic…
Discrete diffusion models based on continuous-time Markov chains (CTMCs) have shown strong performance on language and discrete data generation, yet existing approaches typically parameterize the reverse rate matrix monolithically --…
We investigate the Poisson regression method for Markov and semi-Markov jump processes from a nonparametric angle, allowing the lengths of the time and duration intervals in the partition to vary with the number of observations. Imposing no…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
Markov chain Monte Carlo methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition…
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…
We propose a Bayesian inference approach for a class of latent Markov models. These models are widely used for the analysis of longitudinal categorical data, when the interest is in studying the evolution of an individual unobservable…
Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…
Reversible jump Markov chain Monte Carlo (RJMCMC) proposals that achieve reasonable acceptance rates and mixing are notoriously difficult to design in most applications. Inspired by recent advances in deep neural network-based normalizing…
A possibly time-dependent transition intensity matrix or generator $(Q(t))$ characterizes the law of a Markov jump process (MP). For a time homogeneous MP, the transition probability matrix (TPM) can be expressed as a matrix exponential of…