To discretize continually: Mean shift interacting particle systems for Bayesian inference
Authors: Ayoub Belhadji, Daniel Sharp, Youssef M. Marzouk
Summary
arXiv:2605. 14142v1 Announce Type: new Abstract: Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields.
Relevance
Read next because To discretize continually: Mean shift interacting particle systems for Bayesian inference overlaps with clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "A pretraining-data-poisoned Qwen3-4B backdoor only fires on the exact trigger tokens — paraphrases don't activate it, and base-model similarity to the trigger doesn't predict which inputs fire (MODERATE confidence)". Matching terms: class, rate, implement, trained, model. Source: arxiv stat.ML (Machine Learning).
Threat model
Potential threat/caveat for clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)": this item discusses benchmark.
Abstract
arXiv:2605.14142v1 Announce Type: new Abstract: 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 admit both gradient-free and gradient-informed implementations. The resulting mean shift interacting particle systems converge quickly, capture anisotropy and multi-modality, avoid mode collapse, and scale to high dimensions. We demonstrate their performance on a wide range of benchmark sampling problems, including multi-modal mixtures, Bayesian hierarchical models, PDE-constrained inverse problems, and beyond.