Related papers: A Simple Parallel and Distributed Sampling Techniq…
Many problems in the physical sciences, machine learning, and statistical inference necessitate sampling from a high-dimensional, multi-modal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this…
The Dobrushin comparison theorem is a powerful tool to bound the difference between the marginals of high-dimensional probability distributions in terms of their local specifications. Originally introduced to prove uniqueness and decay of…
We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…
The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is…
Exponential random graph models have become increasingly important in the study of modern networks ranging from social networks, economic networks, to biological networks. They seek to capture a wide variety of common network tendencies…
We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
Sampling from discrete distributions is a ubiquitous task in machine learning, recently revisited by the emergence of discrete diffusion models. While Langevin algorithms constitute the state of the art for continuous spaces, discrete…
Brooks' theorem states that all connected graphs but odd cycles and cliques can be colored with $\Delta$ colors, where $\Delta$ is the maximum degree of the graph. Such colorings have been shown to admit non-trivial distributed algorithms…
An important problem arising in the study of complex networks, for instance in community detection and motif finding, is the sampling of graphs with fixed degree sequence. The equivalent problem of generating random 0,1 matrices with fixed…
Finding effective ways to exploit parallel computing to accelerate Markov chain Monte Carlo methods is an important problem in Bayesian computation and related disciplines. In this paper, we consider the zeroth-order setting where the…
Finding a ground state of a given Hamiltonian is an important but hard problem. One of the potential methods is to use a Markov chain Monte Carlo (MCMC) to sample the Gibbs distribution whose highest peaks correspond to the ground states.…
Approximate random $k$-colouring of a graph $G$ is a well studied problem in computer science and statistical physics. It amounts to constructing a $k$-colouring of $G$ which is distributed close to {\em Gibbs distribution} in polynomial…
Continuum Glauber dynamics is a spatial birth-death process whose stationary distribution is a Gibbs distribution. We establish a spectral gap for Continuum Glauber dynamics applied to Gibbs point processes with repulsive pair potentials, a…
We consider parallel asynchronous Markov Chain Monte Carlo (MCMC) sampling for problems where we can leverage (stochastic) gradients to define continuous dynamics which explore the target distribution. We outline a solution strategy for…
As it has become common to use many computer cores in routine applications, finding good ways to parallelize popular algorithms has become increasingly important. In this paper, we present a parallelization scheme for Markov chain Monte…
MCMC methods (Monte Carlo Markov Chain) are a class of methods used to perform simulations per a probability distribution $P$. These methods are often used when we have difficulties to directly sample per a given probability distribution…
Gibbs sampling is a widely popular Markov chain Monte Carlo algorithm that can be used to analyze intractable posterior distributions associated with Bayesian hierarchical models. There are two standard versions of the Gibbs sampler: The…
Probabilistic graphical models, such as Markov random fields (MRFs), are useful for describing high-dimensional distributions in terms of local dependence structures. The probabilistic inference is a fundamental problem related to graphical…
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…