To discretize continually: Mean shift interacting particle systems for Bayesian inference
Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples -- i.e., a quadrature rule -- constructed via an interacting particle system that minimizes maximum mean discrepancy (MMD) to the target distribution. These methods extend the classical mean shift algorithm, as well as recent algorithms for optimal quantization of empirical distributions, to the case of continuous distributions. Crucially, our approach creates dynamics for MMD minimization that are invariant to the unknown normalizing constant; they also admi...
| Authors | Ayoub Belhadji, Daniel Sharp, Youssef M. Marzouk |
|---|---|
| Primary category | stat.ML |
| Published | 13 May 2026 |
| Last updated at source | 13 May 2026 |
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