# Input Adaptive Bayesian Model Averaging

arXiv: https://arxiv.org/abs/2510.22054 · HTML: https://mlsanity.com/paper/2510.22054/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 50 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Bayesian hierarchical stacking: Some models are (somewhere) useful](https://mlsanity.com/paper/2101.08954/) (2021)
- [Synthetic Model Combination: An Instance-wise Approach to Unsupervised Ensemble Learning](https://mlsanity.com/paper/2210.05320/) (2022)
- [Quantifying Uncertainty in the Presence of Distribution Shifts](https://mlsanity.com/paper/2506.18283/) (2025)

## Abstract (arXiv)

This paper studies prediction with multiple candidate models, where the goal is to combine their outputs. This task is especially challenging in heterogeneous settings, where different models may be better suited to different inputs. We propose input adaptive Bayesian Model Averaging (IA-BMA), a Bayesian method that assigns model weights conditional on the input. IA-BMA employs an input adaptive prior, and yields a posterior distribution that adapts to each prediction, which we estimate with amortized variational inference. We derive formal guarantees for its performance, relative to any single predictor selected per input. We evaluate IABMA across regression and classification tasks, studying data from personalized cancer treatment, credit-card fraud detection, and UCI datasets. IA-BMA consistently delivers more accurate and better-calibrated predictions than both non-adaptive baselines and existing adaptive methods.