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[2402.10758] Stochastic Localization via Iterative Posterior Sampling
Summary
This article presents a novel methodology called Stochastic Localization via Iterative Posterior Sampling (SLIPS) for sampling from unnormalized target densities using stochastic localization techniques.
Why It Matters
The research addresses a significant gap in the application of stochastic localization for sampling, which is crucial for various machine learning tasks. By providing a comprehensive framework and practical guidelines, it enhances the understanding and implementation of sampling methods in complex distributions.
Key Takeaways
- Introduces SLIPS, a new methodology for sampling from unnormalized target densities.
- Explores the use of stochastic localization techniques in machine learning.
- Demonstrates the effectiveness of SLIPS on multi-modal distributions and practical benchmarks.
- Provides detailed guidelines for implementing the proposed sampling method.
- Fills a research gap in the application of stochastic localization in sampling.
Statistics > Machine Learning arXiv:2402.10758 (stat) [Submitted on 16 Feb 2024 (v1), last revised 20 Feb 2026 (this version, v3)] Title:Stochastic Localization via Iterative Posterior Sampling Authors:Louis Grenioux, Maxence Noble, Marylou Gabrié, Alain Oliviero Durmus View a PDF of the paper titled Stochastic Localization via Iterative Posterior Sampling, by Louis Grenioux and 3 other authors View PDF Abstract: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, $\textit{Stochastic Localization via Iterative Posterior Sampling}$ (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 be...
