TY - GEN

T1 - Partially Exchangeable Networks and Architectures for Learning Summary Statistics in Approximate Bayesian Computation

AU - Wiqvist, Samuel

AU - Mattei, Pierre-Alexandre

AU - Picchini, Umberto

AU - Frellsen, Jes

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Deep neural architectures

KW - Partially exchangeable networks (PENs)

KW - Probabilistic symmetries

KW - Block-switch transformations

KW - Approximate Bayesian Computation (ABC)

M3 - Article in proceedings

VL - 97

SP - 6798

EP - 6807

BT - Proceedings of the 36th International Conference on Machine Learning, PMLR

ER -