Partially Exchangeable Networks and Architectures for Learning Summary Statistics in Approximate Bayesian Computation

We present a novel family of deep neural architectures, named partially exchangeable networks (PENs) that leverage probabilistic symmetries. By design, PENs are invariant to block-switch transformations, which characterize the partial exchangeability properties of conditionally Markovian processes....

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Bibliographic Details
Published in:arXiv.org 2019-05
Main Authors: Wiqvist, Samuel, Pierre-Alexandre Mattei, Picchini, Umberto, Frellsen, Jes
Format: Article
Language:English
Subjects:
Bayesian analysis
Computation
Economic models
Invariants
Machine learning
Markov analysis
Markov processes
Pens
Static models
Statistical analysis
Statistical methods
Statistics
Switching theory
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Summary:We present a novel family of deep neural architectures, named partially exchangeable networks (PENs) that leverage probabilistic symmetries. 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.
ISSN:2331-8422