Partially Exchangeable Networks and Architectures for Learning Summary Statistics in Approximate Bayesian Computation
This work addresses the challenge of improving efficiency and reliability in approximate Bayesian computation for researchers in statistics and machine learning, though it appears incremental as it builds on existing architectures like DeepSets.
The authors tackled the problem of learning summary statistics in approximate Bayesian computation by introducing partially exchangeable networks (PENs), which leverage probabilistic symmetries and are invariant to block-switch transformations. Their results show that PENs are highly competitive with previous deep learning methods, providing more reliable posterior samples even with less training data in both time series and static models.
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.