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

Authors

  • Jakob Kruse Heidelberg University
  • Gianluca Detommaso amazon.com
  • Ullrich Köthe University of Heidelberg
  • Robert Scheichl Heidelberg University

Keywords:

Other Foundations of Machine Learning

Abstract

Many recent invertible neural architectures are based on coupling block designs where variables are divided in two subsets which serve as inputs of an easily invertible (usually affine) triangular transformation. While such a transformation is invertible, its Jacobian is very sparse and thus may lack expressiveness. This work presents a simple remedy by noting that subdivision and (affine) coupling can be repeated recursively within the resulting subsets, 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 evaluate our method on some standard data sets and benchmark its full power 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.

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Published

2021-05-18

How to Cite

Kruse, J., Detommaso, G., Köthe, U., & Scheichl, R. (2021). HINT: Hierarchical Invertible Neural Transport for Density Estimation and Bayesian Inference. Proceedings of the AAAI Conference on Artificial Intelligence, 35(9), 8191-8199. Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/16997

Issue

Section

AAAI Technical Track on Machine Learning II