An approximate KLD based experimental design for models with intractable likelihoods

TL;DR

This paper introduces an approximate KLD-based experimental design method for models with intractable likelihoods, using a new utility function based on entropy estimation to enable efficient data collection strategies.

Contribution

The authors develop a lower bound of the KLD utility that can be computed without explicit likelihoods, facilitating experimental design in complex models.

Findings

The proposed method effectively estimates information gain in models with intractable likelihoods.

Numerical examples demonstrate the efficiency and accuracy of the entropy-based utility approximation.

The approach enables practical experimental design where traditional KLD methods are infeasible.

Abstract

Data collection is a critical step in statistical inference and data science, and the goal of statistical experimental design (ED) is to find the data collection setup that can provide most information for the inference. In this work we consider a special type of ED problems where the likelihoods are not available in a closed form. In this case, the popular information-theoretic Kullback-Leibler divergence (KLD) based design criterion can not be used directly, as it requires to evaluate the likelihood function. To address the issue, we derive a new utility function, which is a lower bound of the original KLD utility. This lower bound is expressed in terms of the summation of two or more entropies in the data space, and thus can be evaluated efficiently via entropy estimation methods. We provide several numerical examples to demonstrate the performance of the proposed method.