Normalizing Flows; Bayesian Networks; Density Estimation
Abstract :
[en] Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we
revisit their coupling and autoregressive transformation layers as probabilistic graphical models and show that they reduce to Bayesian networks with a pre-defined topology and a learnable density at each node. From this new perspective, we provide three results. First, we show that stacking multiple transformations in a normalizing flow relaxes independence assumptions and entangles the model distribution. Second, we show that a fundamental leap of capacity emerges when the depth of affine flows exceeds 3 transformation layers. Third, we prove the non-universality of the affine normalizing flow, regardless of its depth.
Disciplines :
Computer science
Author, co-author :
Wehenkel, Antoine ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Big Data
Louppe, Gilles ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Big Data
Language :
English
Title :
You say Normalizing Flows I see Bayesian Networks
Publication date :
10 July 2020
Number of pages :
Antoine Wehenkel
Event name :
ICML2020 Workshop on Invertible Neural Networks, Normalizing Flows, and Explicit Likelihood Models
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