Related papers: Toward Unlimited Self-Learning MCMC with Parallel …

The performance of sequential Monte Carlo (SMC) samplers heavily depends on the tuning of the Markov kernels used in the path proposal. For SMC samplers with unadjusted Markov kernels, standard tuning objectives, such as the…

We present a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis for differential equations. This is in contrast to classical…

Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with…

We propose Continual Repeated Annealed Flow Transport Monte Carlo (CRAFT), a method that combines a sequential Monte Carlo (SMC) sampler (itself a generalization of Annealed Importance Sampling) with variational inference using normalizing…

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…

The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…

This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…

One of the major problems in adaptive filtering is the problem of system identification. It has been studied extensively due to its immense practical importance in a variety of fields. The underlying goal is to identify the impulse response…

In this study, we propose quantum annealing-enhanced Markov Chain Monte Carlo (QAEMCMC), where QA is integrated into the MCMC subroutine. QA efficiently explores low-energy configurations and overcomes local minima, enabling the generation…

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…

Monte Carlo (MC) sampling algorithms are an extremely widely-used technique to estimate expectations of functions f(x), especially in high dimensions. Control variates are a very powerful technique to reduce the error of such estimates, but…

We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly…

Spectral subsampling MCMC was recently proposed to speed up Markov chain Monte Carlo (MCMC) for long stationary univariate time series by subsampling periodogram observations in the frequency domain. This article extends the approach to…

Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…

We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…

Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models…

In the era of Big Data, Markov chain Monte Carlo (MCMC) methods, which are currently essential for Bayesian estimation, face significant computational challenges owing to their sequential nature. To achieve a faster and more effective…

This work presents self-rewarding sequential Monte Carlo (SMC), an inference-time scaling algorithm enabling effective sampling of masked diffusion language models (MDLMs). Our algorithm stems from the observation that most existing MDLMs…

A formal mean square error expansion (MSE) is derived for Euler--Maruyama numerical solutions of stochastic differential equations (SDE). The error expansion is used to construct a pathwise a posteriori adaptive time stepping…