Robust Experimental Design via Generalised Bayesian Inference
This work addresses the issue of model misspecification in experimental design for researchers and practitioners in statistics and machine learning, offering a robust alternative to traditional Bayesian methods.
The paper tackles the problem of Bayesian optimal experimental design being sensitive to model misspecification by introducing Generalised Bayesian Optimal Experimental Design (GBOED), which uses a loss function instead of a likelihood for robustness, and demonstrates enhanced robustness to outliers and incorrect noise assumptions in empirical results.
Bayesian optimal experimental design is a principled framework for conducting experiments that leverages Bayesian inference to quantify how much information one can expect to gain from selecting a certain design. However, accurate Bayesian inference relies on the assumption that one's statistical model of the data-generating process is correctly specified. If this assumption is violated, Bayesian methods can lead to poor inference and estimates of information gain. Generalised Bayesian (or Gibbs) inference is a more robust probabilistic inference framework that replaces the likelihood in the Bayesian update by a suitable loss function. In this work, we present Generalised Bayesian Optimal Experimental Design (GBOED), an extension of Gibbs inference to the experimental design setting which achieves robustness in both design and inference. Using an extended information-theoretic framework, we derive a new acquisition function, the Gibbs expected information gain (Gibbs EIG). Our empirical results demonstrate that GBOED enhances robustness to outliers and incorrect assumptions about the outcome noise distribution.