Causal Effect Estimation under Networked Interference without Networked Unconfoundedness Assumption

TL;DR

This work tackles the problem of estimating causal effects under networked interference when latent confounders are present and the networked unconfoundedness assumption may not hold. It develops a confounder recovery framework that identifies three latent confounder types ($U^i$, $U^c$, $U^n$) using identifiable representation learning, proving their identifiability and disentanglement. Building on these results, the authors introduce CaLaNet, a three-module estimator (representation learning, feature aggregation, and outcome prediction) that leverages GCNs and ELBO-based training with score matching and IPM balancing to identify and estimate networked effects. The method is validated on semisynthetic BlogCatalog and Flickr datasets and a synthetic dataset, showing superior performance over baselines in both average and individual effects and demonstrating accurate latent confounder recovery, thus enabling networked causal inference without the networked unconfoundedness assumption.

Abstract

Estimating causal effects under networked interference from observational data is a crucial yet challenging problem. Most existing methods mainly rely on the networked unconfoundedness assumption, which guarantees the identification of networked effects. However, this assumption is often violated due to the latent confounders inherent in observational data, thereby hindering the identification of networked effects. To address this issue, we leverage the rich interaction patterns between units in networks, which provide valuable information for recovering these latent confounders. Building on this insight, we develop a confounder recovery framework that explicitly characterizes three categories of latent confounders in networked settings: those affecting only the unit, those affecting only the unit's neighbors, and those influencing both. Based on this framework, we design a networked effect estimator using identifiable representation learning techniques. From a theoretical standpoint, we prove the identifiability of all three types of latent confounders and, by leveraging the recovered confounders, establish a formal identification result for networked effects. Extensive experiments validate our theoretical findings and demonstrate the effectiveness of the proposed method.

Figures (6)

• Figure 1: d A simple example illustrating network interference among three units. The networked interference introduces interactions between units, represented by the solid red arrows. These interactions violate the traditional SUTVA assumption, rendering the network effects non-identifiable.
• Figure 2: Assumed causal graph in this paper. $x$ denotes observed proxies, $u$ denotes latent confounders, $t$ denotes the treatment, and $y$ denotes the outcome of interest. We assume that latent confounders $u$ contain three types of variables, i.e., $u^i$ affecting the unit itself, $u^n$ affecting the unit's neighbors, and $u^c$ affecting both.
• Figure 3: Model architecture of our proposed method named CaLaNet. The representation learning module aims to learn the latent confounders. The feature module aggregates the information of the confounders of unit $i$ and its neighbor. The outcome estimator module aims to estimate potential outcomes of unit $i$.
• Figure 4: The figure presents scatter plots visualizing the relationship between the recovered latent confounders and ground-truth latent confounders $U^i, U^c$, and $U^n$.
• Figure 5: Hyperparameter sensitivity result regarding individual effect estimation error on BC(homo) dataset.

Theorems & Definitions (5)

• Definition 1: Average Effects
• Definition 2: Individual Effects
• Theorem 1
• Theorem 2
• Theorem 3