Peer Effect Estimation in the Presence of Simultaneous Feedback and Unobserved Confounders

Estimating peer causal effects within complex real-world networks such as social networks is challenging, primarily due to simultaneous feedback between peers and unobserved confounders. Existing methods either address unobserved confounders while ignoring the simultaneous feedback, or account for feedback but under restrictive linear assumptions, thus failing to obtain accurate peer effect estimation. In this paper, we propose DIG2RSI, a novel Deep learning framework which leverages I-G transformation (matrix operation) and 2SRI (an instrumental variable or IV technique) to address both simultaneous feedback and unobserved confounding, while accommodating complex, nonlinear and high-dimensional relationships. DIG2RSI first applies the I-G transformation to disentangle mutual peer influences and eliminate the bias due to the simultaneous feedback. To deal with unobserved confounding, we first construct valid IVs from network data. In stage 1 of 2RSI, we train a neural network on these IVs to predict peer exposure, and extract residuals as proxies for the unobserved confounders. In the stage 2, we fit a separate neural network augmented by an adversarial discriminator that incorporates these residuals as a control function and enforces the learned representation to contain no residual confounding signal. The expressive power of deep learning models in capturing complex non-linear relationships and adversarial debiasing enhances the effectiveness of DIG2RSI in eliminating bias from both feedback loops and hidden confounders. We prove consistency of our estimator under standard regularity conditions, ensuring asymptotic recovery of the true peer effect. Empirical results on two semi-synthetic benchmarks and a real-world dataset demonstrate that DIG2RSI outperforms existing approaches.