Inferring Individual Direct Causal Effects Under Heterogeneous Peer Influence

TL;DR

This work tackles the problem of estimating unit-level direct causal effects in networks with heterogeneous peer influence (HPI) when the mechanism is unknown. It introduces IDE-Net, a framework that combines a Network Structural Causal Model (NSCM) with a Network Abstract Ground Graph (NAGG) to formalize identifiability under diverse HPI contexts. IDE-Net uses expressive graph neural network embeddings to capture potential confounders and effect modifiers, along with a counterfactual outcome predictor and a variance-smoothing regularization to stabilize unit-level effects. Empirical results on synthetic and semi-synthetic networks demonstrate that IDE-Net is robust to unknown HPI mechanisms and outperforms state-of-the-art methods that assume homogeneous peer influence. The approach advances personalized intervention design in networks by enabling reliable causal effect estimation under complex interference patterns.

Abstract

Causal inference in networks should account for interference, which occurs when a unit's outcome is influenced by treatments or outcomes of peers. Heterogeneous peer influence (HPI) occurs when a unit's outcome is influenced differently by different peers based on their attributes and relationships, or when each unit has a different susceptibility to peer influence. Existing solutions to estimating direct causal effects under interference consider either homogeneous influence from peers or specific heterogeneous influence mechanisms (e.g., based on local neighborhood structure). This paper presents a methodology for estimating individual direct causal effects in the presence of HPI where the mechanism of influence is not known a priori. We propose a structural causal model for networks that can capture different possible assumptions about network structure, interference conditions, and causal dependence and enables reasoning about identifiability in the presence of HPI. We find potential heterogeneous contexts using the causal model and propose a novel graph neural network-based estimator to estimate individual direct causal effects. We show that state-of-the-art methods for individual direct effect estimation produce biased results in the presence of HPI, and that our proposed estimator is robust.

Figures (10)

• Figure 1: Overview of the IDE-Net framework through an example query of whether a user's political affiliation (X) affects the user's stance (Y). NSCM, like structural equation model, encodes the domain and data assumptions (e.g., homophily and selection bias) and NAGG, like a graphical model, enables causal reasoning to find a maximal adjustment set of relational variables, if the IDE is identifiable. The IDE Estimator uses a GNN-based feature representation of the maximal adjustment set and network features and it learns to predict counterfactual outcomes.
• Figure 2: Two ego networks with the same number of treated and untreated friends but possibly different peer exposure conditions.
• Figure 3: Relational paths (i.e., traversal in the schema) for a toy social network. The paths capture an ego, the ego's relationships, other nodes, and their relationships (except with the ego).
• Figure 4: Estimation error for IDEs with effect modification and HPI based on similarity, mutual connections, and peer degree.
• Figure 5: $\epsilon_{PEHE}$ errors for constant true individual direct effects and heterogeneous peer influence.

Theorems & Definitions (26)

• Definition 1: Heterogeneous Peer Influence (HPI)
• Definition 2: Relational skeleton with relationship existence
• Definition 3: Relationship existence indicator
• Lemma 1
• Proposition 2
• Lemma 3
• Corollary 4
• Theorem 5
• Corollary 6
• Theorem 7