Graphical Residual Flows

Jacobie Mouton, Rodney Stephen Kroon

Keywords: Normalizing flow, Bayesian network, density estimation, inference

TL;DR: This work introduces graphical residual flows which encode an arbitrary Bayesian network dependency structure in an invertible residual network to provide a competitive graphical flow with stable inversion.

Abstract: Graphical flows add further structure to normalizing flows by encoding non-trivial variable dependencies. Previous graphical flow models have focused primarily on a single flow direction: the normalizing direction for density estimation, or the generative direction for inference. However, to use a single flow to perform tasks in both directions, the model must exhibit stable and efficient flow inversion. This work introduces graphical residual flows, a graphical flow based on invertible residual networks. Our approach to incorporating dependency information in the flow, means that we are able to calculate the Jacobian determinant of these flows exactly. Our experiments confirm that graphical residual flows provide stable and accurate inversion that is also more time-efficient than alternative flows with similar task performance. Furthermore, our model provides performance competitive with other graphical flows for both density estimation and inference tasks.