Graphical Residual Flows

TL;DR

Graphical residual flows leverage invertible residual networks to encode variable dependencies, enabling stable, efficient, and exact inversion for density estimation and inference, with competitive performance.

Contribution

This paper introduces graphical residual flows based on invertible residual networks, allowing exact Jacobian determinant calculation and improved stability and efficiency in flow inversion.

Findings

Stable and accurate flow inversion achieved.

More time-efficient than alternative flows.

Performance competitive with existing graphical flows.

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.