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arXiv · 2007.05426

Variational Inference with Continuously-Indexed Normalizing Flows

Anthony Caterini·Rob Cornish·Dino Sejdinovic·Arnaud Doucet
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Abstract

Continuously-indexed flows (CIFs) have recently achieved improvements over baseline normalizing flows on a variety of density estimation tasks. CIFs do not possess a closed-form marginal density, and so, unlike standard flows, cannot be plugged in directly to a variational inference (VI) scheme in order to produce a more expressive family of approximate posteriors. However, we show here how CIFs can be used as part of an auxiliary VI scheme to formulate and train expressive posterior approximations in a natural way. We exploit the conditional independence structure of multi-layer CIFs to build the required auxiliary inference models, which we show empirically yield low-variance estimators of the model evidence. We then demonstrate the advantages of CIFs over baseline flows in VI problems when the posterior distribution of interest possesses a complicated topology, obtaining improved results in both the Bayesian inference and surrogate maximum likelihood settings.

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Anthony Caterini, Rob Cornish, Dino Sejdinovic, Arnaud Doucet. 2020-07-10. Variational Inference with Continuously-Indexed Normalizing Flows. https://arxiv.org/abs/2007.05426

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