# Representative, Informative, and De-Amplifying: Requirements for Robust Bayesian Active Learning under Model Misspecification

arXiv: https://arxiv.org/abs/2506.07805 · HTML: https://mlsanity.com/paper/2506.07805/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 79 references that are in the map.
- First posted on arXiv 9 Jun 2025.

## Builds on (most cited first, 28 of 28)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [Learning Active Learning from Data](https://mlsanity.com/paper/1703.03365/) (2017)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [On Statistical Bias In Active Learning: How and When To Fix It](https://mlsanity.com/paper/2101.11665/) (2021)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)
- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024)
- [Maximum Likelihood Estimation is All You Need for Well-Specified Covariate Shift](https://mlsanity.com/paper/2311.15961/) (2023)
- [Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference](https://mlsanity.com/paper/2301.11674/) (2023)
- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)
- [Bayesian optimization with known experimental and design constraints for chemistry applications](https://mlsanity.com/paper/2203.17241/) (2022)
- [Bayesian inference for misspecified generative models](https://mlsanity.com/paper/2305.08429/) (2023)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [Bayesian decision-theoretic design of experiments under an alternative model](https://mlsanity.com/paper/1909.12570/) (2019)
- [Characterizing the robustness of Bayesian adaptive experimental designs to active learning bias](https://mlsanity.com/paper/2205.13698/) (2022)
- [Metrics for Bayesian Optimal Experiment Design under Model Misspecification](https://mlsanity.com/paper/2304.07949/) (2023)
- [Bayesian Active Learning in the Presence of Nuisance Parameters](https://mlsanity.com/paper/2310.14968/) (2023)
- [Reliable Bayesian Inference in Misspecified Models](https://mlsanity.com/paper/2302.06031/) (2023)
- [Mitigating Covariate Shift in Misspecified Regression with Applications to Reinforcement Learning](https://mlsanity.com/paper/2401.12216/) (2024)
- [Minimizing Sensitivity to Model Misspecification](https://mlsanity.com/paper/1807.02161/) (2018)
- [Partial Wasserstein and Maximum Mean Discrepancy distances for bridging the gap between outlier detection and drift detection](https://mlsanity.com/paper/2106.12893/) (2021)
- [Gibbs optimal design of experiments](https://mlsanity.com/paper/2310.17440/) (2023)

## Built on by (most cited first, 2 of 2)

- [Constrained Bayesian Experimental Design via Online Planning](https://mlsanity.com/paper/2605.26990/) (2026)
- [Learning to Outgrow a Theory: Experimental Discovery Beyond the Initial Hypothesis Space](https://mlsanity.com/paper/2610.07627/) (2026)

## Abstract (arXiv)

In many science and industry settings, a central challenge is designing experiments under time and budget constraints. Bayesian Optimal Experimental Design (BOED) is a paradigm to pick maximally informative designs that has been widely applied to such problems. During training, BOED selects inputs according to a pre-determined acquisition criterion to target informativeness. During testing, the model learned during training encounters a naturally occurring distribution of test samples. This leads to an instance of covariate shift, where the train and test samples are drawn from different distributions (the training samples are not representative of the test distribution). Prior work has shown that in the presence of model misspecification, covariate shift amplifies generalization error. Our first contribution is to provide a mathematical analysis of generalization error in the presence of model misspecification, revealing that, beyond covariate shift, generalization error is also driven by a previously unidentified phenomenon we term error (de-)amplification. We then develop a new acquisition function that mitigates the effects of model misspecification by including terms for representativeness, informativeness, and de-amplification (R-IDeA). Our experimental results demonstrate that the proposed method performs better than methods that target only informativeness, only representativeness, or both.