Treatment-Aware Hyperbolic Representation Learning for Causal Effect Estimation with Social Networks

TL;DR

This work tackles ITE estimation from networked observational data by addressing hidden confounding tied to social network structure. It introduces TAHyper, which combines hyperbolic space embedding (via the Poincaré ball, exponential/log maps, and Hyperbolic Graph Convolutional Networks) with a treatment-aware relationship identification module to capture both macro-scale network structure and micro-scale treatment-related patterns. The model predicts potential outcomes with dual regression heads and uses IPM-based distribution balancing to mitigate covariate shift, yielding an objective $\mathcal{L}=\mathcal{L}_y+\alpha\mathcal{L}_t+\beta\mathcal{D}(k,q)+\lambda\|\theta\|_2^2$. Empirical results on BlogCatalog and Flickr show TAHyper consistently outperforms baselines across various confounding levels, with ablation confirming the necessity of both hyperbolic representation and treatment-aware learning. This approach improves causal effect estimation in networked data and offers a scalable framework for real-world domains where scale-free network structure and treatment-related neighbor patterns matter.

Abstract

Estimating the individual treatment effect (ITE) from observational data is a crucial research topic that holds significant value across multiple domains. How to identify hidden confounders poses a key challenge in ITE estimation. Recent studies have incorporated the structural information of social networks to tackle this challenge, achieving notable advancements. However, these methods utilize graph neural networks to learn the representation of hidden confounders in Euclidean space, disregarding two critical issues: (1) the social networks often exhibit a scalefree structure, while Euclidean embeddings suffer from high distortion when used to embed such graphs, and (2) each ego-centric network within a social network manifests a treatment-related characteristic, implying significant patterns of hidden confounders. To address these issues, we propose a novel method called Treatment-Aware Hyperbolic Representation Learning (TAHyper). Firstly, TAHyper employs the hyperbolic space to encode the social networks, thereby effectively reducing the distortion of confounder representation caused by Euclidean embeddings. Secondly, we design a treatment-aware relationship identification module that enhances the representation of hidden confounders by identifying whether an individual and her neighbors receive the same treatment. Extensive experiments on two benchmark datasets are conducted to demonstrate the superiority of our method.

Figures (4)

• Figure 1: Left: Node degree distribution in two benchmark datasets (BlogCatalog and Flickr); Right: An illustrative example of treatment-related relationships.
• Figure 2: The causal diagram (h is hidden confounders).
• Figure 3: Overview of Our Method (TAHyper).
• Figure 4: Hyperparameter study on BlogCatalog.

Theorems & Definitions (1)

• Definition 3.1