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Individualized Causal Effects under Network Interference with Combinatorial Treatments

Yunping Lu, Haoang Chi, Qirui Hu, Zhiheng Zhang

TL;DR

This work builds a unified framework that constructs a global potential-outcome emulator for unit-level inference in high-dimensional networked settings and shows that individualized causal inference remains feasible in high-dimensional networked settings without collapsing the intervention space.

Abstract

Modern causal decision-making increasingly demands individualized treatment-effect estimation in networks where interventions are high-dimensional, combinatorial vectors. While network interference, effect heterogeneity, and multi-dimensional treatments have been studied separately, their intersection yields an exponentially large intervention space that makes standard identification tools and low-dimensional exposure mappings untenable. We bridge this gap with a unified framework that constructs a \emph{global potential-outcome emulator} for unit-level inference. Our method combines (1) rooted network configurations to leverage local smoothness, (2) doubly robust orthogonalization to mitigate confounding from network position and covariates, and (3) sparse spectral learning to efficiently estimate response surfaces over the $2^p$-dimensional treatment space. We also decompose networked effects into own-treatment, structural, and interaction components, and provide finite-sample error bounds and asymptotic consistency guarantees. Overall, we show that individualized causal inference remains feasible in high-dimensional networked settings without collapsing the intervention space.

Individualized Causal Effects under Network Interference with Combinatorial Treatments

TL;DR

This work builds a unified framework that constructs a global potential-outcome emulator for unit-level inference in high-dimensional networked settings and shows that individualized causal inference remains feasible in high-dimensional networked settings without collapsing the intervention space.

Abstract

Modern causal decision-making increasingly demands individualized treatment-effect estimation in networks where interventions are high-dimensional, combinatorial vectors. While network interference, effect heterogeneity, and multi-dimensional treatments have been studied separately, their intersection yields an exponentially large intervention space that makes standard identification tools and low-dimensional exposure mappings untenable. We bridge this gap with a unified framework that constructs a \emph{global potential-outcome emulator} for unit-level inference. Our method combines (1) rooted network configurations to leverage local smoothness, (2) doubly robust orthogonalization to mitigate confounding from network position and covariates, and (3) sparse spectral learning to efficiently estimate response surfaces over the -dimensional treatment space. We also decompose networked effects into own-treatment, structural, and interaction components, and provide finite-sample error bounds and asymptotic consistency guarantees. Overall, we show that individualized causal inference remains feasible in high-dimensional networked settings without collapsing the intervention space.
Paper Structure (31 sections, 9 theorems, 60 equations, 2 figures, 2 algorithms)

This paper contains 31 sections, 9 theorems, 60 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formalization
  3. Illustrative example.
  4. Identification
  5. Identification via local orthogonal moments
  6. Estimation
  7. Localized weighted Lasso for Walsh coefficients
  8. Debiased inference for an own-treatment contrast
  9. Theoretical analysis
  10. What this theorem says (and what it does not).
  11. Experiments
  12. Evolution of the proposed estimator
  13. Conclusion
  14. Simulation setup
  15. Proofs for Section \ref{['sec:theory']}
  16. ...and 16 more sections

Key Result

Theorem 3.1

Assume Assumptions 2.1--2.4. Fix a target pair $(g,x)$ in the interior of the support. Then there exists a (possibly localized) coefficient vector $\alpha^\star(g,x)$ such that Moreover, under the local overlap condition in Assumption 2.3, $\alpha^\star(g,x)$ is unique within the model class implied by Assumption 2.4 (e.g., the sparse/near-sparse cone), and it identifies the response function in

Figures (2)

  • Figure 1: Comparison of point estimates and 95% confidence intervals in synthetic experiments ($N=500$, 100 independent repetitions). Our proposed method (width 0.233, bias 0.031) substantially outperforms the baseline (0.486, 0.124) and approaches the oracle (0.087, -0.007), providing empirical evidence for Theorems 5.2 and 5.5.
  • Figure 2: Convergence of the Localized DR-Lasso Estimator. Boxplots display the sampling distribution across 100 simulations for each sample size. The horizontal axis indicates the total sample size $N$; the vertical axis measures relative estimation error (normalized to zero). Top annotations: Sample mean $\pm$ standard deviation; Center: Sample median (red line); Bottom: Empirical 95% confidence interval width ($W = Q_{97.5} - Q_{2.5}$).

Theorems & Definitions (17)

  • Theorem 3.1: Identification of localized Walsh coefficients
  • Corollary 3.2: Identification of individualized contrasts
  • Lemma 5.1: Orthogonalization remainder
  • Theorem 5.2: Finite-sample error for localized weighted Lasso
  • Corollary 5.3: Plug-in error for individualized contrasts
  • Remark 5.4
  • Theorem 5.5: Asymptotic normality of the debiased contrast
  • Lemma 2.1: Convex-hull bound for $m(g,x)$
  • proof
  • Lemma 2.2: Weighted sub-Gaussian maximal inequality
  • ...and 7 more