Ricci Curvature, Robustness, and Causal Inference on Networked Data

TL;DR — This paper explores the relationship between graph curvature and causal inference in networks, showing that positive curvature regions lead to more accurate causal effect estimation from graph neural networks.

Abstract

In the complex landscape of networked data, understanding the causal effects of interventions is a critical challenge with implications across various domains. Graph Neural Networks (GNNs) have emerged as a powerful tool for capturing complex dependencies, yet the potential of geometric deep learning for GNN-based network causal inference remains underexplored. This work makes three key contributions to bridge this gap. First, we establish a theoretical connection between graph curvature and causal inference, revealing that negative curvatures pose challenges in identifying causal effects. Second, based on this theoretical insight, we present computational results using Ricci curvature to predict the reliability of causal effect estimations, empirically demonstrating that positive curvature regions yield more accurate estimations. Lastly, we propose a method using Ricci flow to improve treatment effect estimation on networked data, showing superior performance by reducing error through flattening the edges in the network. Our findings open new avenues for leveraging geometry in causal effect estimation, offering insights and tools that enhance the performance of GNNs in causal inference tasks.