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This paper aims at improving the convergence to equilibrium of finite ergodic Markov chains via permutations and projections. First, we prove that a specific mixture of permuted Markov chains arises naturally as a projection under the KL…

Probability · Mathematics 2025-07-22 Michael C. H. Choi , Max Hird , Youjia Wang

We show that the minimax sample complexity for estimating the pseudo-spectral gap $\gamma_{\mathsf{ps}}$ of an ergodic Markov chain in constant multiplicative error is of the order of $$\tilde{\Theta}\left( \frac{1}{\gamma_{\mathsf{ps}}…

Statistics Theory · Mathematics 2023-08-07 Geoffrey Wolfer , Aryeh Kontorovich

Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a…

Methodology · Statistics 2019-10-30 Christopher Nemeth , Fredrik Lindsten , Maurizio Filippone , James Hensman

The present paper focuses on the problem of sampling from a given target distribution $\pi$ defined on some general state space. To this end, we introduce a novel class of non-reversible Markov chains, each chain being defined on an…

Computation · Statistics 2023-05-16 Randal Douc , Alain Durmus , Aurélien Enfroy , Jimmy Olsson

Markov chain Monte Carlo (MCMC) methods to sample from a probability distribution $\pi$ defined on a space $(\Theta,\mathcal{T})$ consist of the simulation of realisations of Markov chains $\{\theta_{n},n\geq1\}$ of invariant distribution…

Computation · Statistics 2021-01-06 Christophe Andrieu , Sinan Yıldırım , Arnaud Doucet , Nicolas Chopin

We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The…

Statistical Mechanics · Physics 2016-03-23 Rüdiger Kürsten , Ulrich Behn

We consider the computational task of sampling a bit string $x$ from a distribution $\pi(x)=|\langle x|\psi\rangle|^2$, where $\psi$ is the unique ground state of a local Hamiltonian $H$. Our main result describes a direct link between the…

Quantum Physics · Physics 2023-11-09 Sergey Bravyi , Giuseppe Carleo , David Gosset , Yinchen Liu

In the field of sampling algorithms, MCMC (Markov Chain Monte Carlo) methods are widely used when direct sampling is not possible. However, multimodality of target distributions often leads to slow convergence and mixing. One common…

Machine Learning · Computer Science 2023-04-05 Holden Lee , Zeyu Shen

Sampling from Gibbs distribution is a central problem in computer science as well as in statistical physics. In this work we focus on the k-colouring model} and the hard-core model with fugacity \lambda when the underlying graph is an…

Discrete Mathematics · Computer Science 2017-01-24 Charilaos Efthymiou

Exponential random graphs are used extensively in the sociology literature. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of triangles and other small subgraphs.…

Probability · Mathematics 2008-12-15 Shankar Bhamidi , Guy Bresler , Allan Sly

I introduce a Markov chain Monte Carlo (MCMC) scheme in which sampling from a distribution with density pi(x) is done using updates operating on an "ensemble" of states. The current state x is first stochastically mapped to an ensemble,…

Computation · Statistics 2011-01-04 Radford M. Neal

The spectral gap $\gamma$ of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to…

Statistics Theory · Mathematics 2017-08-25 Daniel Hsu , Aryeh Kontorovich , David A. Levin , Yuval Peres , Csaba Szepesvári

Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target…

In this paper, selection of an active sensor subset for tracking a discrete time, finite state Markov chain having an unknown transition probability matrix (TPM) is considered. A total of N sensors are available for making observations of…

Machine Learning · Computer Science 2020-11-02 Mrigank Raman , Ojal Kumar , Arpan Chattopadhyay

Slice Sampling has emerged as a powerful Markov Chain Monte Carlo algorithm that adapts to the characteristics of the target distribution with minimal hand-tuning. However, Slice Sampling's performance is highly sensitive to the…

Machine Learning · Statistics 2021-10-05 Minas Karamanis , Florian Beutler

Markov Chain Monte Carlo (MCMC) underlies both statistical physics and combinatorial optimization, but mixes slowly near critical points and in rough landscapes. Parallel Tempering (PT) improves mixing by swapping replicas across…

Machine Learning · Computer Science 2025-09-30 Saleh Bunaiyan , Corentin Delacour , Shuvro Chowdhury , Kyle Lee , Kerem Y. Camsari

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…

Machine Learning · Statistics 2016-12-09 Jost Tobias Springenberg , Aaron Klein , Stefan Falkner , Frank Hutter

The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in enhancing phase space mixing of these protocols, thus…

Statistical Mechanics · Physics 2011-12-06 John D. Chodera , Michael R. Shirts

In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and…

Computation · Statistics 2023-12-22 Björn Sprungk , Simon Weissmann , Jakob Zech

A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions,…

Machine Learning · Computer Science 2020-09-10 Rong Ge , Holden Lee , Andrej Risteski