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Variational Inference with Normalizing Flows

Variational Inference with Normalizing FlowsDanilo Jimenez DeepMind, LondonAbstractThe choice of approximate posterior distributionis one of the core problems in Variational infer-ence. Most applications of Variational inferenceemploy simple families of posterior approxima-tions in order to allow for efficient Inference , fo-cusing on mean-field or other simple structuredapproximations. This restriction has a signifi-cant impact on the quality of inferences madeusing Variational methods. We introduce a newapproach for specifying flexible, arbitrarily com-plex and scalable approximate posterior distribu-tions. Our approximations are distributions con-structed through a Normalizing flow, whereby asimple initial density is transformed into a morecomplex one by applying a sequence of invertibletransformations until a desired level of complex-ity is attained. We use this view of normalizingflows to develop categories of finite and infinites-imal Flows and provide a unified view of ap-proaches for constructing rich posterior approxi-mations.

provement in performance (Mnih & Gregor,2014). There is also a large body of evidence that describes the detri-mental effect of limited posterior approximations.Turner & Sahani(2011) provide an exposition of two commonly experienced problems. The first is the widely-observed problem of under-estimation of the variance of the poste-

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