Stochastic Gradient Bayesian Optimal Experimental Designs for Simulation Based Inference

Published: 20 Jun 2023, Last Modified: 17 Sept 2023Differentiable Almost EverythingEveryoneRevisionsBibTeX
Keywords: bayesian optimal experimental design, variational inference, generative modeling, normalizing flows, biology, systems biology
TL;DR: We describe a method for implementing gradient-based optimization of experimental designs for simulation-based inference models, which is advantageous in high dimensions over conventional bayesian optimization.
Abstract: Simulation-based inference (SBI) methods tackle complex scientific models with challenging inverse problems. However, SBI models often face a significant hurdle due to their non-differentiable nature, which hampers the use of gradient-based optimization techniques. Bayesian Optimal Experimental Design (BOED) is a powerful approach that aims to make the most efficient use of experimental resources for improved inferences. While stochastic gradient BOED methods have shown promising results in high-dimensional design problems, they have mostly neglected the integration of BOED with SBI due to the difficult non-differentiable property of many SBI simulators. In this work, we establish a crucial connection between ratio-based SBI inference algorithms and stochastic gradient-based variational inference by leveraging mutual information bounds. This connection allows us to extend BOED to SBI applications, enabling the simultaneous optimization of experimental designs and amortized inference functions. We demonstrate our approach on a simple linear model and offer implementation details for practitioners.
Submission Number: 53