Viscos Flows: Variational Schur Conditional Sampling With Normalizing Flows

TL;DR

This paper introduces a novel variational Schur conditional sampling method for pre-trained normalizing flows, enabling efficient inference with partial observations by leveraging Gaussian properties and bijective domain partitioning.

Contribution

It provides new insights on variational distribution selection, domain partitioning to maintain bijectivity, and optimization techniques for the proposed sampling method.

Findings

Effective conditional sampling on invertible residual networks

Preserves bijectivity through domain partitioning

Achieves accurate inference and classification results

Abstract

We present a method for conditional sampling for pre-trained normalizing flows when only part of an observation is available. We derive a lower bound to the conditioning variable log-probability using Schur complement properties in the spirit of Gaussian conditional sampling. Our derivation relies on partitioning flow's domain in such a way that the flow restrictions to subdomains remain bijective, which is crucial for the Schur complement application. Simulation from the variational conditional flow then amends to solving an equality constraint. Our contribution is three-fold: a) we provide detailed insights on the choice of variational distributions; b) we discuss how to partition the input space of the flow to preserve bijectivity property; c) we propose a set of methods to optimise the variational distribution. Our numerical results indicate that our sampling method can be successfully applied to invertible residual networks for inference and classification.