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Convergence diagnosis for Markov chain Monte Carlo is a matter of fundamental importance in computational statistics: it determines the resources allocated to a particular sampling problem and influences the practitioner's view of the…

We introduce a framework for efficient Markov Chain Monte Carlo (MCMC) algorithms targeting discrete-valued high-dimensional distributions, such as posterior distributions in Bayesian variable selection (BVS) problems. We show that many…

Markov chain Monte Carlo (MCMC) algorithms are indispensable when sampling from a complex, high-dimensional distribution by a conventional method is intractable. Even though MCMC is a powerful tool, it is also hard to control and tune in…

Markov chain Monte Carlo (MCMC) methods are one of the most popular classes of algorithms for sampling from a target probability distribution. A rising trend in recent years consists in analyzing the convergence of MCMC algorithms using…

We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed…

We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…

A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and…

Uniform sampling of binary matrix with fixed margins is an important and difficult problem in statistics, computer science, ecology and so on. The well-known swap algorithm would be inefficient when the size of the matrix becomes large or…

Subgraph-wise sampling -- a promising class of mini-batch training techniques for graph neural networks (GNNs -- is critical for real-world applications. During the message passing (MP) in GNNs, subgraph-wise sampling methods discard…

We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we proof a pivotal convergence theorem for finite Markov chains and a minimal version of the…

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…

In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such…

In this article we propose a novel MCMC method based on deterministic transformations T: X x D --> X where X is the state-space and D is some set which may or may not be a subset of X. We refer to our new methodology as Transformation-based…

Recent advances in stochastic gradient techniques have made it possible to estimate posterior distributions from large datasets via Markov Chain Monte Carlo (MCMC). However, when the target posterior is multimodal, mixing performance is…

Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by…

Markov chain Monte Carlo (MCMC) is the predominant tool used in Bayesian parameter estimation for hierarchical models. When the model expands due to an increasing number of hierarchical levels, number of groups at a particular level, or…

We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is…

Markov chain Monte Carlo (MCMC) methods provide powerful framework for sampling unknown probability measures across a wide range of scientific applications. In some settings, the target distribution is supported on a lower-dimensional…

Invention involves combination, or more precisely, ratios of composition. According to Thomas Edison, "Genius is one percent inspiration and 99 percent perspiration" is an example. In many situations, researchers and inventors already have…

Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the…