Related papers: Sequential Controlled Langevin Diffusions
We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (projected) LMC allows to sample in polynomial time from a…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…
We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling…
Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…
Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…
Score-based generative models (SGMs) have demonstrated remarkable synthesis quality. SGMs rely on a diffusion process that gradually perturbs the data towards a tractable distribution, while the generative model learns to denoise. The…
Sequential Monte Carlo (SMC), or particle filtering, is a popular class of methods for sampling from an intractable target distribution using a sequence of simpler intermediate distributions. Like other importance sampling-based methods,…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte Carlo methods. We study here an advanced version of familiar Markov Chain Monte…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
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…
In this paper, we provide non-asymptotic upper bounds on the error of sampling from a target density using three schemes of discretized Langevin diffusions. The first scheme is the Langevin Monte Carlo (LMC) algorithm, the Euler…
Sequential Monte Carlo Squared (SMC$^2$) is a Bayesian method which can infer the states and parameters of non-linear, non-Gaussian state-space models. The standard random-walk proposal in SMC$^2$ faces challenges, particularly with…
Diffusion models (DMs) have emerged as powerful image priors in Bayesian computational imaging. Two primary strategies have been proposed for leveraging DMs in this context: Plug-and-Play methods, which are zero-shot and highly flexible but…
We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…
Langevin Monte Carlo (LMC) is a popular Bayesian sampling method. For the log-concave distribution function, the method converges exponentially fast, up to a controllable discretization error. However, the method requires the evaluation of…
We show how to speed up Sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is…
We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured…