Unifying Summary Statistic Selection for Approximate Bayesian Computation

Understand

Extracting low-dimensional summary statistics from large datasets is essential for efficient (likelihood-free) inference.

• We characterize three different classes of summaries and demonstrate their importance for correctly analyzing dimensionality reduction algorithms.
• We demonstrate that minimizing the expected posterior entropy (EPE) under the prior predictive distribution of the model provides a unifying principle that subsumes many existing methods; they are shown to be equivalent to, or special or limiting cases of, minimizing the EPE.
• We offer a unifying framework for obtaining informative summaries and propose a practical method using conditional density estimation to learn high-fidelity summaries automatically.