In this talk, we will introduce partially exchangeable networks (PENs) [1], and we will, inparticular, discuss the application of learning summary statistics for approximate Bayesiancomputation (ABC). Connections between our methodology and other deep learning-basedmethods  for  simulation  inference  will  also  be  highlighted.   By  design,  PENs  are  invariantto  block-switch  transformations,  which  characterize  the  partial  exchangeability  propertiesof conditionally Markovian processes.  More- over, we show that any block-switch invariantfunction has a PEN-like representation.  The DeepSets architecture is a special case of PENand we can therefore also target fully exchangeable data. We employ PENs to learn summarystatistics in ABC. When comparing PENs to previous deep learning methods for learningsummary  statistics,  our  results  are  highly  competitive,  both  considering  time  series  andstatic models.  In- deed, PENs provide more reliable posterior samples even when using lesstraining data.This is joint work with Umberto Picchini and Jes Frellsen.
 

[1]  S. Wiqvist, P.-A. Mattei, U. Picchini, and J. Frellsen. Partially exchangeable networksand architectures for learning summary statistics in approximate Bayesian computation.In Proceedings of the 36th International Conference on Machine Learning. PMLR, 2019.http://proceedings.mlr.press/v97/wiqvist19a/wiqvist19a.pdf