Beyond Global Divergences: A Local-Mass Perspective on Bayesian Inference
Quick summary
arXiv:2606.27090v2 Announce Type: replace-cross Abstract: 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 characteris
Key takeaways
- arXiv:2606.27090v2 Announce Type: replace-cross Abstract: 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.
Why it matters
The value of this work lies as much in how it was tested as in the claim itself. Sample design, baselines, uncertainty and replication help separate a laboratory result from real-world impact.
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