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

Many recent invertible neural architectures are based on coupling block designs where variables divided in two subsets which serve as inputs of an easily (usually affine) triangular transformation. While such a transformation is invertible, its Jacobian very sparse and thus may lack expressiveness. This work presents simple remedy by noting that subdivision (affine) can be repeated recursively within the resulting subsets, leading to efficiently with dense, Jacobian. By formulating our recursive scheme via hierarchical architecture, HINT allows sampling from joint distribution p(y,x) corresponding posterior p(x|y) using single network. We evaluate method some standard data sets benchmark full power for density estimation Bayesian inference novel set 2D shapes Fourier parameterization, enables consistent visualization samples different dimensionalities.