相关论文: On the complexity of standard and waste-free SMC s…

We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global…

We present bounds for the finite sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties…

We prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the $L_2$ distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first…

Simulated tempering is a widely used strategy for sampling from multimodal distributions. In this paper, we consider simulated tempering combined with an arbitrary local Markov chain Monte Carlo sampler and present a new decomposition…

The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…

A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings,…

We develop a modular approach to Markov chain Monte Carlo (MCMC) sampling for unnormalized target densities. In this approach, Markov chains are constructed in parallel, each constrained to a subset of the target space. The Monte Carlo…

We study the basic task of mean estimation in the presence of mean-shift contamination. In the mean-shift contamination model, an adversary is allowed to replace a small constant fraction of the clean samples by samples drawn from…

We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using…

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…

We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending on local rather than global Markov chain mixing dynamics.…

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…

In this paper, we provide bounds on the asymptotic variance for a class of sequential Monte Carlo (SMC) samplers designed for approximating multimodal distributions. Such methods combine standard SMC methods and Markov chain Monte Carlo…

Multimodal structures in the sampling density (e.g. two competing phases) can be a serious problem for traditional Markov Chain Monte Carlo (MCMC), because correct sampling of the different structures can only be guaranteed for infinite…

We prove non-asymptotic error bounds for Sequential MCMC methods in the case of multimodal target distributions. Our bounds depend in an explicit way on upper bounds on relative densities, on constants associated with local mixing…

In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…

This paper addresses finite sample stability properties of sequential Monte Carlo methods for approximating sequences of probability distributions. The results presented herein are applicable in the scenario where the start and end…

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…

We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…

Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…