2024/02/16 by Louis Grenioux, Maxence Noble, Grenioux, Louis +5 · 4 citations
Computer Science · #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.2402.10758
openalex publication_date 2024/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Building upon score-based learning, new interest in stochastic localization techniques has recently emerged. In these models, one seeks to noise a sample from the data distribution through a stochastic process, called observation process, and progressively learns a denoiser associated to this dynamics. Apart from specific applications, the use of stochastic localization for the problem of sampling from an unnormalized target density has not been explored extensively. This work contributes to fill this gap. We consider a general stochastic localization framework and introduce an explicit class of observation processes, associated with flexible denoising schedules. We provide a complete methodology, Stochastic Localization via Iterative Posterior Sampling (SLIPS), to obtain approximate samples of this dynamics, and as a by-product, samples from the target distribution. Our scheme is based on a Markov chain Monte Carlo estimation of the denoiser and comes with detailed practical guidelines. We illustrate the benefits and applicability of SLIPS on several benchmarks of multi-modal distributions, including Gaussian mixtures in increasing dimensions, Bayesian logistic regression and a high-dimensional field system from statistical-mechanics.