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Title: Partially exchangeable networks and architectures for learning summary statistics in approximate Bayesian computation Authors:  Samuel Wiqvist - University of Lund (Sweden)
Pierre-Alexandre Mattei - INRIA, Universite Cote d'Azur (France) [presenting]
Umberto Picchini - Chalmers University of Technology and University of Gothenburg (Sweden)
Jes Frellsen - Technical University of Denmark (Denmark)
Abstract: A novel family of deep neural architectures, named Partially Exchangeable Networks (PENs) that leverage probabilistic symmetries, is presented. By design, PENs are invariant to block-switch transformations, which characterize the partial exchangeability properties of conditionally Markovian processes. Moreover, we show that any block-switch invariant function has a PEN-like representation. The DeepSets architecture is a special case of PEN and we can therefore also target fully exchangeable data. We employ PENs to learn summary statistics in approximate Bayesian computation (ABC). When comparing PENs to previous deep learning methods for learning summary statistics, our results are highly competitive, both considering time series and static models. Indeed, PENs provide more reliable posterior samples even when using less training data.