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We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin…

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has been increasingly popular in Bayesian learning due to its ability to deal with large data. A standard SG-MCMC algorithm simulates samples from a discretized-time Markov chain to…

Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…

This paper introduces the R package sgmcmc; which can be used for Bayesian inference on problems with large datasets using stochastic gradient Markov chain Monte Carlo (SGMCMC). Traditional Markov chain Monte Carlo (MCMC) methods, such as…

Variational Monte Carlo (VMC) is an approach for computing ground-state wavefunctions that has recently become more powerful due to the introduction of neural network-based wavefunction parametrizations. However, efficiently training neural…

Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and…

Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…

We present doubly stochastic gradient MCMC, a simple and generic method for (approximate) Bayesian inference of deep generative models (DGMs) in a collapsed continuous parameter space. At each MCMC sampling step, the algorithm randomly…

We present the Monte Carlo with Absorbing Markov Chains (MCAMC) method for extremely long kinetic Monte Carlo simulations. The MCAMC algorithm does not modify the system dynamics. It is extremely useful for models with discrete state spaces…

Due to the need for robust uncertainty quantification, Bayesian neural learning has gained attention in the era of deep learning and big data. Markov Chain Monte-Carlo (MCMC) methods typically implement Bayesian inference which faces…

Sequential Monte Carlo (SMC) methods represent a classical set of techniques to simulate a sequence of probability measures through a simple selection/mutation mechanism. However, the associated selection functions and mutation kernels…

Adaptive and interacting Markov Chains Monte Carlo (MCMC) algorithms are a novel class of non-Markovian algorithms aimed at improving the simulation efficiency for complicated target distributions. In this paper, we study a general…

Designing efficient learning algorithms with complexity guarantees for Markov decision processes (MDPs) with large or continuous state and action spaces remains a fundamental challenge. We address this challenge for entropy-regularized MDPs…

We present Generative Monte Carlo (GMC), a novel paradigm for particle transport simulation that integrates generative artificial intelligence directly into the stochastic solution of the linear Boltzmann equation. By reformulating the…

Bayesian variable selection requires sampling from a posterior distribution that combines discrete model indicators with continuously varying parameters, a challenge often addressed through reversible jump Markov chain Monte Carlo (RJMCMC).…

This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…

Markov Chain Monte Carlo (MCMC) is a powerful method for drawing samples from non-standard probability distributions and is utilized across many fields and disciplines. Methods such as Metropolis-Adjusted Langevin (MALA) and Hamiltonian…

We consider conditional tests for non-negative discrete exponential families. We develop two Markov Chain Monte Carlo (MCMC) algorithms which allow us to sample from the conditional space and to perform approximated tests. The first…

We present an adaptive multi-GPU Exchange Monte Carlo method designed for the simulation of the 3D Random Field Model. The algorithm design is based on a two-level parallelization scheme that allows the method to scale its performance in…