Learning Regularization for Graph Inverse Problems

TL;DR

This paper introduces a novel framework combining GNNs with likelihood and prior terms to effectively solve Graph Inverse Problems, especially when direct observations of graph properties are unavailable or noisy.

Contribution

The paper proposes a new GNN-based framework for GRIP that integrates deep inverse problem techniques with learned priors, addressing indirect and noisy measurements.

Findings

Framework effectively solves various GRIPs

Demonstrates improved accuracy over baseline methods

Applicable to diverse graph-related inverse problems

Abstract

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph directly; instead, noisy and indirect measurements of these properties are available. These scenarios are coined as Graph Inverse Problems (GRIP). In this work, we introduce a framework leveraging GNNs to solve GRIPs. The framework is based on a combination of likelihood and prior terms, which are used to find a solution that fits the data while adhering to learned prior information. Specifically, we propose to combine recent deep learning techniques that were developed for inverse problems, together with GNN architectures, to formulate and solve GRIP. We study our approach on a number of representative problems that demonstrate the effectiveness of the framework.