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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.

Variational Inference with Normalizing Flows tion). For example, if q ˚(z) is a Gaussian distribution N(zj ;˙ 2), with ˚= f ;˙g, then the location-scale transformation using the standard Normal as a base distribution allows us to reparameterize z as:

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  Inference, Variational, Variational inference

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