Invertible Neural Networks for Graph Prediction

TL;DR

This paper introduces invertible graph neural networks (iGNN) that enable both forward prediction and inverse data inference on graphs, leveraging invertible mappings and optimal transport theory for scalable, expressive graph modeling.

Contribution

We develop a novel invertible GNN framework that efficiently handles inverse prediction tasks on graphs using invertible mappings, regularization, and theoretical insights from optimal transport.

Findings

Effective inverse prediction demonstrated on synthetic and real data.

Scalability achieved for large graphs with factorized mixture models.

Theoretical foundations established for invertible graph mappings.

Abstract

Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop \textit{invertible graph neural network} (iGNN), a deep generative model to tackle the inverse prediction problem on graphs by casting it as a conditional generative task. The proposed model consists of an invertible sub-network that maps one-to-one from data to an intermediate encoded feature, which allows forward prediction by a linear classification sub-network as well as efficient generation from output labels via a parametric mixture model. The invertibility of the encoding sub-network is ensured by a Wasserstein-2 regularization which allows free-form layers in the residual blocks. The model is scalable to large graphs by a factorized parametric mixture model of the encoded feature and is computationally scalable by using GNN layers. The existence of invertible flow mapping is backed by theories of optimal transport and diffusion process, and we prove the expressiveness of graph convolution layers to approximate the theoretical flows of graph data. The proposed iGNN model is experimentally examined on synthetic data, including the example on large graphs, and the empirical advantage is also demonstrated on real-application datasets of solar ramping event data and traffic flow anomaly detection.