Variational Bayesian Optimal Experimental Design (1903.05480v3)

Abstract: Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information gain (EIG) of an experiment. To address this, we introduce several classes of fast EIG estimators by building on ideas from amortized variational inference. We show theoretically and empirically that these estimators can provide significant gains in speed and accuracy over previous approaches. We further demonstrate the practicality of our approach on a number of end-to-end experiments.

• The paper proposes variational inference techniques that significantly boost computational efficiency and convergence rates in Expected Information Gain estimation.
• It introduces distinct variational estimators (VPO, VMO, VNMC, and VML) tailored to different contexts in experimental design.
• Empirical validations across adaptive experiments demonstrate the practical potential in fields like neuroscience, bioinformatics, and psychology.

Variational Bayesian Optimal Experimental Design

The paper "Variational Bayesian Optimal Experimental Design" introduces novel methodologies to enhance the efficiency and accuracy of estimating the Expected Information Gain (EIG) within the framework of Bayesian Optimal Experimental Design (OED). Traditional methods of EIG estimation, particularly Nested Monte Carlo (NMC), often suffer from high computational costs and poor convergence rates due to the complexity inherent in nested expectation problems. By leveraging variational inference techniques, the authors propose a suite of EIG estimators that offer substantial improvements in computational efficiency and accuracy, presenting a significant advancement in the field of experimental design.

The authors articulate the challenge that conventional NMC methods face—a convergence rate limited to 𝒪(𝑇^{-1/3})—and propose faster converging variational approaches. The core innovation lies in the use of amortized variational inference, which allows for shared information across different experimental outcomes, fundamentally altering the computational landscape for EIG estimation. The proposed variational methodologies, namely the variational posterior estimator (𝒱𝑃𝑂), the variational marginal (𝒱𝑀𝑂), the variational NMC (𝒱𝑁𝑀𝐶), and the variational marginal and likelihood (𝒱𝑀𝐿), each present distinct advantages depending on the problem context, such as the dimensionality of the latent space or whether an explicit likelihood is available.

The theoretical underpinning of these approaches is bolstered by rigorous proofs of their convergence properties. The authors demonstrate that these variational estimators can achieve convergence rates up to 𝒪(𝑇^{-1/2}), a marked improvement over existing methods. This enhancement allows for the practical applicability of OED methodologies in real-time and adaptive experimental settings, which is demonstrated through empirical validation across multiple experimental design scenarios, including A/B testing, preference learning, mixed effects models, and more.

In terms of practical implications, the proposed variational estimators are particularly well-suited for application in fields requiring adaptive sequential experiment designs, such as neuroscience, bioinformatics, psychology, and beyond. The ability to reduce computational overhead while improving the accuracy of information gain estimates opens new avenues for complex experimental setups that were previously computationally prohibitive.

The integration of these methods into probabilistic programming frameworks like Pyro suggests an easier adoption and testing by the broader research community, allowing for a streamlined process to implement and test Bayesian optimal designs without significant overhead in developing custom solutions.

Looking forward, this work not only enhances current capabilities in OED but also poses intriguing questions for further research, particularly in optimizing variational families and exploring their performance in highly complex and high-dimensional problems. Future inquiry may delve into automated selection methodologies for variational families or hybrid approaches that combine the strengths of multiple estimators tailored to specific design requirements. The proposed techniques offer a fertile ground for both theoretical exploration and practical application across diverse domains seeking optimal experimental strategies.