When: 29th September,
1.30pm UK time
Speaker: Till
Hoffmann (Harward T.H. Chan School of Publich Health)
Title: Minimizing the Expected Posterior Entropy Yields Optimal Summary Statistics
Abstract: Extracting low-dimensional summary statistics from large datasets is essential for
efficient (likelihood-free) inference. We propose obtaining summary statistics by minimizing the expected posterior entropy (EPE) under the prior predictive distribution of the model. We show that minimizing the EPE is equivalent to learning a conditional
density estimator for the posterior as well as other information-theoretic approaches. Further summary extraction methods (including minimizing the Lē Bayes risk, maximizing the Fisher information, and model selection approaches) are special or limiting cases
of EPE minimization. We demonstrate that the approach yields high fidelity summary statistics by applying it to both a synthetic benchmark as well as a population genetics problem. We not only offer concrete recommendations for practitioners but also provide
a unifying perspective for obtaining informative summary statistics.
Reference: T. Hoffmann and J.P. Onnela. Minimizing the Expected Posterior Entropy Yields Optimal
Summary Statistics. Preprint at ArXiv:2206.02340, 2022