Related papers: Distance between configurations in Markov chain Mo…
For a given Markov chain Monte Carlo (MCMC) algorithm, we define the distance between configurations that quantifies the difficulty of transitions. This distance enables us to investigate MCMC algorithms in a geometrical way, and we…
In our previous work [1], we introduced to an arbitrary Markov chain Monte Carlo algorithm a distance between configurations. This measures the difficulty of transition from one configuration to the other, and enables us to investigate the…
We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by…
Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the…
Manifold Markov chain Monte Carlo algorithms have been introduced to sample more effectively from challenging target densities exhibiting multiple modes or strong correlations. Such algorithms exploit the local geometry of the parameter…
Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating…
This review paper, written for the second edition of the Handbook of Markov Chain Monte Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte Carlo (MCMC), aimed at researchers new to the field. We…
Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…
We prove results on the decidability and complexity of computing the total variation distance (equivalently, the $L_1$-distance) of hidden Markov models (equivalently, labelled Markov chains). This distance measures the difference between…
We propose a new Markov chain Monte Carlo method in which trial configurations are generated by evolving a state, sampled from a prior distribution, using a Markov transition matrix. We present two prototypical algorithms and derive their…
Adaptive Markov Chain Monte Carlo (AMCMC) is a class of MCMC algorithms where the proposal distribution changes at every iteration of the chain. In this case it is important to verify that such a Markov Chain indeed has a stationary…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…
In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint…
Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…
A number of problems in a variety of fields are characterised by target distributions with a multimodal structure in which the presence of several isolated local maxima dramatically reduces the efficiency of Markov Chain Monte Carlo…
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…
The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…
Motivated by information geometry, a distance function on the space of stochastic matrices is advocated. Starting with sequences of Markov chains the Bhattacharyya angle is advocated as the natural tool for comparing both short and long…
Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…