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

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 vertical bar 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.

Automated summary

This work introduces a method for invertible neural architectures using coupling block designs, achieving an efficiently invertible block with dense, triangular Jacobian by recursively subdividing and coupling within resulting subsets. Through a hierarchical architecture, the method allows sampling from joint distributions and corresponding posteriors using a single invertible network, demonstrating its effectiveness in density estimation and Bayesian inference on various data sets.