Graph Machine Learning based Doubly Robust Estimator for Network Causal Effects

TL;DR

The paper tackles causal inference in social networks under interference and high-dimensional confounding by marrying graph neural networks with a doubly robust, semi-parametric inference framework. It develops a GDML approach that learns nuisance functions with GNNs and uses a Neyman orthogonal score within a cross-fitted focal-set procedure to estimate the average direct effect and average peer effect with valid confidence intervals. The authors prove consistency and asymptotic normality under regularity conditions and demonstrate scalability and robustness through semi-synthetic benchmarks on Cora, PubMed, Flickr, and a real Self-Help Group case in India. They also discuss identifiability, provide detailed theoretical derivations, and offer extensive complementary experiments to validate the framework and its generality across nuisance estimators and graph densities.

Abstract

We address the challenge of inferring causal effects in social network data. This results in challenges due to interference -- where a unit's outcome is affected by neighbors' treatments -- and network-induced confounding factors. While there is extensive literature focusing on estimating causal effects in social network setups, a majority of them make prior assumptions about the form of network-induced confounding mechanisms. Such strong assumptions are rarely likely to hold especially in high-dimensional networks. We propose a novel methodology that combines graph machine learning approaches with the double machine learning framework to enable accurate and efficient estimation of direct and peer effects using a single observational social network. We demonstrate the semiparametric efficiency of our proposed estimator under mild regularity conditions, allowing for consistent uncertainty quantification. We demonstrate that our method is accurate, robust, and scalable via an extensive simulation study. We use our method to investigate the impact of Self-Help Group participation on financial risk tolerance.

Figures (4)

• Figure 1: Partial causal graph of a network with three nodes. The left side shows the network topology, and the right side depicts the causal graph for each node with $\mathcal{X}$, $\mathbf{T}$, and $\mathbf{Y}$ as confounder, treatment, and outcome, respectively. Solid circles represent endogenous variables; dotted circles, exogenous. Blue edges indicate within-unit confounding, green edges show neighbor confounding, red edges represent direct effects, and yellow edges denote treatment interference.
• Figure 2: Framework schema. The focal set is partitioned into train and estimation folds $I_{-k}$ and $I_k$ for cross-fitting. Propensity score and outcome models are learned over $I_{-k}$ using graph machine learning. Estimations of $\mathbb{E}[T \mid X, A]$ and $\mathbb{E}[Y \mid X, A]$ for $I_k$ are computed to derive residuals $resT$, $resPE$, and $resY$. Finally, $resY$ is regressed on $resT$ and $resPE$ to obtain $\hat{\theta_k}$ and $\hat{\alpha_k}$ for ADE and APE. This process is repeated across folds, and results are aggregated for final estimations of $\theta$ and $\alpha$.
• Figure 3: Relative Error of different methods for estimating causal effects across different datasets. Note that the y-axis is log-scaled. In the figure, two variants of our method are presented: one utilizing a focal set and another without a focal set, encompassing the entire dataset. 'PA' refers to Double Machine Learning combined with predefined aggregates
• Figure 4: Relative error of SBM for different $P_{intra}$ with $3000$ nodes, $200$ components and $P_{inter} = 0.0001$

Theorems & Definitions (4)

• Proposition 3.1
• Definition 4.1
• Theorem 5.2
• Proposition 10.2