HINT: Hierarchical Invertible Neural Transport for Density Estimation and Bayesian Inference

Jakob Kruse, Gianluca Detommaso, Robert Scheichl, Ullrich Köthe

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

20 Citations (SciVal)

Abstract

A large proportion of recent invertible neural architectures is based on a coupling block design. It operates by dividing incoming variables into two sub-spaces, one of which parameterizes an easily invertible (usually affine) transformation that is applied to the other. While the Jacobian of such a transformation is triangular, it is very sparse and thus may lack expressiveness. This work presents a simple remedy by noting that (affine) coupling can be repeated recursively within the resulting sub-spaces, leading to an efficiently invertible block with dense triangular Jacobian. By formulating our recursive coupling scheme via a hierarchical architecture, HINT allows sampling from a joint distribution p(y,x) and the corresponding posterior p(x|y) using a single invertible network. We demonstrate the power of our method for density estimation and Bayesian inference on a novel data set of 2D shapes in Fourier parameterization, which enables consistent visualization of samples for different dimensionalities.
Original languageEnglish
Title of host publicationProceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI-21)
Pages8191-8199
Volume35
Edition9
DOIs
Publication statusPublished - 18 May 2021

Publication series

NameProceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI-21)
PublisherAssociation for the Advancement of Artificial Intelligence (AAAI)

Keywords

  • stat.ML
  • cs.AI
  • cs.LG

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