Related papers: Sampling with Shielded Langevin Monte Carlo Using …

We introduce a new Markov chain Monte Carlo (MCMC) sampler for infinite-dimensional inverse problems. Our new sampler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of…

We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel…

Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…

The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational…

We describe a new MCMC method optimized for the sampling of probability measures on Hilbert space which have a density with respect to a Gaussian; such measures arise in the Bayesian approach to inverse problems, and in conditioned…

Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows…

There has been considerable interest in designing Markov chain Monte Carlo algorithms by exploiting numerical methods for Langevin dynamics, which includes Hamiltonian dynamics as a deterministic case. A prominent approach is Hamiltonian…

Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) algorithm for estimating expectations with respect to continuous un-normalized probability distributions. MCMC estimators typically have higher variance than…

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses…

There is a neglected fact in the traditional machine learning methods that the data sampling can actually lead to the solution sampling. We consider this observation to be important because having the solution sampling available makes the…

Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…

Random samples of quantum states with specific properties are useful for various applications, such as Monte Carlo integration over the state space. In the high-dimensional situations that one encounters already for a few qubits, the…

We propose Annealed Langevin Monte Carlo for Flow ODE Sampling (ALMC-ODE), a method for generating samples from unnormalized target distributions, with a particular emphasis on multimodal densities that are challenging for standard Markov…

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…

The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…

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…

We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…

Numerous capability and safety techniques of Large Language Models (LLMs), including RLHF, automated red-teaming, prompt engineering, and infilling, can be cast as sampling from an unnormalized target distribution defined by a given reward…