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Novel Monte Carlo methods to generate samples from a target distribution, such as a posterior from a Bayesian analysis, have rapidly expanded in the past decade. Algorithms based on Piecewise Deterministic Markov Processes (PDMPs),…

Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…

Motivated by the problem of exploring discrete but very complex state spaces in Bayesian models, we propose a novel Markov Chain Monte Carlo search algorithm: the taxicab sampler. We describe the construction of this sampler and discuss how…

This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. Firstly, the spectral gap for the…

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…

In recent decades, a number of profound theorems concerning approximation of hard counting problems have appeared. These include estimation of the permanent, estimating the volume of a convex polyhedron, and counting (approximately) the…

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure,…

Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…

Efficient sampling of two-dimensional statistical physics systems remains a central challenge in computational statistical physics. Traditional Markov chain Monte Carlo (MCMC) methods, including cluster algorithms, provide only partial…

We introduce a novel Entropy-driven Monte Carlo (EdMC) strategy to efficiently sample solutions of random Constraint Satisfaction Problems (CSPs). First, we extend a recent result that, using a large-deviation analysis, shows that the…

We define very large-scale multiobjective optimization problems as optimizing multiple objectives (VLSMOPs) with more than 100,000 decision variables. These problems hold substantial significance, given the ubiquity of real-world scenarios…

We study the benefits and limits of parallelised Markov chain Monte Carlo (MCMC) sampling in cosmology. MCMC methods are widely used for the estimation of cosmological parameters from a given set of observations and are typically based on…

We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for…

For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare…

There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…

Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential…

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…