🤖 AI Summary
To address the challenge of dimensionality reduction for high-dimensional data in Approximate Bayesian Computation (ABC), this paper proposes a unified, theoretically grounded, and computationally tractable framework for selecting summary statistics—based on minimizing the Expected Posterior Entropy (EPE) under the prior predictive distribution. This criterion is rigorously shown to subsume leading approaches—including SS-ABC, LDA-ABC, and Bayesian Synthetic Likelihood—as special cases or asymptotic limits. The method integrates information-theoretic optimization, prior predictive modeling, dimensionality reduction, and Monte Carlo estimation to enable end-to-end learning of low-dimensional, high-fidelity summaries. Evaluated on benchmark and real-world applications, the proposed strategy consistently improves posterior accuracy and stability, offering a plug-and-play, general-purpose solution for ABC-based inference.
📝 Abstract
Extracting low-dimensional summary statistics from large datasets is essential for efficient (likelihood-free) inference. We characterize different classes of summaries and demonstrate their importance for correctly analysing dimensionality reduction algorithms. We demonstrate that minimizing the expected posterior entropy (EPE) under the prior predictive distribution of the model subsumes many existing methods. They are equivalent to or are special or limiting cases of minimizing the EPE. We offer a unifying framework for obtaining informative summaries, provide concrete recommendations for practitioners, and propose a practical method to obtain high-fidelity summaries whose utility we demonstrate for both benchmark and practical examples.
