# Bayesian Model Averaging under Predictor Redundancy via Density-Ratio Posterior Compression

arXiv: https://arxiv.org/abs/2606.21080 · HTML: https://mlsanity.com/paper/2606.21080/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 22 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [Comparison of Bayesian predictive methods for model selection](https://mlsanity.com/paper/1503.08650/) (2015)
- [Projective Inference in High-dimensional Problems: Prediction and Feature Selection](https://mlsanity.com/paper/1810.02406/) (2018)
- [Using reference models in variable selection](https://mlsanity.com/paper/2004.13118/) (2020)
- [Model-based clustering of categorical data based on the Hamming distance](https://mlsanity.com/paper/2212.04746/) (2022)

## Abstract (arXiv)

Bayesian model averaging in support-indexed regression induces a posterior distribution over active predictor supports. Under predictor redundancy, posterior mass can spread across many nearly interchangeable supports, making exact-support summaries unstable or hard to interpret even when prediction is stable. We study how to report an already fitted Bayesian model averaging posterior without changing the Bayesian target. A report uses hard or soft regions of support space, and its compressed reporting law is compared with the reference posterior through an explicit density ratio. This ratio gives computable total-variation and Kullback--Leibler distortion, bounds for bounded predictive summaries, retained-mass diagnostics, and fallback-weight diagnostics. The framework covers fixed hard regions, metric-ball regions, posterior-cluster regions, and pooled-pruned region dictionaries. We prove exact error formulas and validation bounds for these region reports, and give conditions under which a few regions can replace a long list of individual supports. In simulations, our region reports often give shorter and clearer summaries while preserving the main posterior information, and the density-ratio diagnostics show when too much information has been lost.