Efficient Bayesian Experimental Design for Implicit Models
This work addresses a largely unexplored problem in experimental design for researchers dealing with implicit models, offering incremental improvements over existing methods.
The paper tackles the challenge of Bayesian experimental design for implicit models, where likelihoods are intractable, by introducing a framework that uses mutual information as a utility function and Bayesian optimization, resulting in increased efficiency and the ability to handle higher design dimensions.
Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible, this task is particularly difficult and therefore largely unexplored. This is mainly due to technical difficulties associated with approximating posterior distributions and utility functions. We devise a novel experimental design framework for implicit models that improves upon previous work in two ways. First, we use the mutual information between parameters and data as the utility function, which has previously not been feasible. We achieve this by utilising Likelihood-Free Inference by Ratio Estimation (LFIRE) to approximate posterior distributions, instead of the traditional approximate Bayesian computation or synthetic likelihood methods. Secondly, we use Bayesian optimisation in order to solve the optimal design problem, as opposed to the typically used grid search or sampling-based methods. We find that this increases efficiency and allows us to consider higher design dimensions.