A Hybrid Gradient Method to Designing Bayesian Experiments for Implicit Models

TL;DR

This paper introduces a hybrid gradient method combining variational MI estimation and evolution strategies to improve Bayesian experimental design for implicit models, enabling scalable and efficient optimization without pathwise sampling.

Contribution

It proposes a novel hybrid gradient approach that overcomes the limitations of previous methods by removing the need for pathwise sampling in implicit models.

Findings

Significantly improves scalability for high-dimensional design spaces.

Enables efficient MI maximization without pathwise sampling.

Demonstrates superior performance in experiments with implicit models.

Abstract

Bayesian experimental design (BED) aims at designing an experiment to maximize the information gathering from the collected data. The optimal design is usually achieved by maximizing the mutual information (MI) between the data and the model parameters. When the analytical expression of the MI is unavailable, e.g., having implicit models with intractable data distributions, a neural network-based lower bound of the MI was recently proposed and a gradient ascent method was used to maximize the lower bound. However, the approach in Kleinegesse et al., 2020 requires a pathwise sampling path to compute the gradient of the MI lower bound with respect to the design variables, and such a pathwise sampling path is usually inaccessible for implicit models. In this work, we propose a hybrid gradient approach that leverages recent advances in variational MI estimator and evolution strategies (ES) combined with black-box stochastic gradient ascent (SGA) to maximize the MI lower bound. This allows the design process to be achieved through a unified scalable procedure for implicit models without sampling path gradients. Several experiments demonstrate that our approach significantly improves the scalability of BED for implicit models in high-dimensional design space.