An approximate KLD based experimental design for models with intractable likelihoods
This work addresses a specific bottleneck in experimental design for statisticians and data scientists dealing with complex models, but it is incremental as it builds on existing KLD-based methods.
The authors tackled the problem of statistical experimental design for models with intractable likelihoods by deriving a new utility function as a lower bound of the Kullback-Leibler divergence, which can be evaluated efficiently via entropy estimation methods, and demonstrated its performance through numerical examples.
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.