Related papers: On Hamiltonian Monte Carlo for Gaussian Random Var…

Langevin algorithms are popular Markov chain Monte Carlo (MCMC) methods for large-scale sampling problems that often arise in data science. We propose Monte Carlo algorithms based on the discretizations of $P$-th order Langevin dynamics for…

We report on a new variant of the hybrid Monte Carlo algorithm employing a polynomial approximation of the inverse of the non-Hermitian Dirac-Wilson operator. Our approximation relies on simple and stable recurrence relations of complex…

Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite…

Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance…

Markov chain Monte Carlo (MCMC) methods have existed for a long time and the field is well-explored. The purpose of MCMC methods is to approximate a distribution through repeated sampling; most MCMC algorithms exhibit asymptotically optimal…

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…

We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…

In this paper, we study Hamiltonian operators which are sum of a first order operator and of a Poisson tensor, in two spatial independent variables. In particular, a complete classification of these operators is presented in two and three…

We generalize the Hamiltonian Monte Carlo algorithm with a stack of neural network layers and evaluate its ability to sample from different topologies in a two dimensional lattice gauge theory. We demonstrate that our model is able to…

Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…

We propose a new framework of variance-reduced Hamiltonian Monte Carlo (HMC) methods for sampling from an $L$-smooth and $m$-strongly log-concave distribution, based on a unified formulation of biased and unbiased variance reduction…

We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a…

We present a scalable Bayesian framework for the analysis of confocal fluorescence spectroscopy data, addressing key limitations in traditional fluorescence correlation spectroscopy methods. Our framework captures molecular motion,…

Markov Chain Monte Carlo (MCMC) methods are a popular technique in Bayesian statistical modeling. They have long been used to obtain samples from posterior distributions, but recent research has focused on the scalability of these…

Galilean invariance is usually violated in self-consistent mean-field calculations that employ effective density-dependent nuclear forces. We present a novel approach, based on variational quantum Monte Carlo techniques, suitable to…

Hierarchical modeling provides a framework for modeling the complex interactions typical of problems in applied statistics. By capturing these relationships, however, hierarchical models also introduce distinctive pathologies that quickly…

We present a nonlinear (in the sense of McKean) generalization of Hamiltonian Monte Carlo (HMC) termed nonlinear HMC (nHMC) capable of sampling from nonlinear probability measures of mean-field type. When the underlying confinement…

Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice. Unfortunately,…

Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized…

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…