Beyond Global Divergences: A Local-Mass Perspective on Bayesian Inference
Global objectives, such as KL divergence and ELBO, are widely used in Bayesian inference for measuring distributional discrepancy. This paper studies distributional ``local-mass behaviours'' that are not directly captured by such global objectives. We introduce and use two mathematical tools: (1) Mass Index for recording the polynomial and logarithmic decay scales of local mass, and (2) regularised extended KL (RE-KL), a set-localised divergence that can be formulated in the presence of singular components. Mass Indices help characterise how Bayesian updating changes local mass: (1) power-log likelihood factors shift it explicitly, and (2) parameter-dependent supports, or their smooth sof...
| Authors | Hanli Xu, Fengxiang He, Sarat Moka |
|---|---|
| Primary category | stat.ML |
| Published | 25 June 2026 |
| Last updated at source | 2 October 2026 |
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