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Causal Influence Maximization with Steady-State Guarantees

Renjie Cao, Zhuoxin Yan, Xinyan Su, Zhiheng Zhang

Abstract

Influence maximization in networks is a central problem in machine learning and causal inference, where an intervention on a subset of individuals triggers a diffusion process through the network. Existing approaches typically optimize short-horizon rewards or rely on strong parametric assumptions, offering limited guarantees for longrun causal outcomes. In this work, we address the problem of selecting a seed set to maximize the total steady-state potential outcome under budget constraints. Theoretically, we demonstrate that under a low-probability propagation assumption, the high-dimensional path-dependent dynamics can be compressed into a low-dimensional exposure mapping with a bounded second-order approximation error. Leveraging this structural reduction, we propose CIM, a two-stage framework that first learns shape-constrained exposureresponse functions from observational data and then optimizes the objective via a greedy strategy. Our approach bridges causal inference with network optimization, providing provable guarantees for both the estimation of outcome functions and the approximation ratio of the influence maximization.

Causal Influence Maximization with Steady-State Guarantees

Abstract

Influence maximization in networks is a central problem in machine learning and causal inference, where an intervention on a subset of individuals triggers a diffusion process through the network. Existing approaches typically optimize short-horizon rewards or rely on strong parametric assumptions, offering limited guarantees for longrun causal outcomes. In this work, we address the problem of selecting a seed set to maximize the total steady-state potential outcome under budget constraints. Theoretically, we demonstrate that under a low-probability propagation assumption, the high-dimensional path-dependent dynamics can be compressed into a low-dimensional exposure mapping with a bounded second-order approximation error. Leveraging this structural reduction, we propose CIM, a two-stage framework that first learns shape-constrained exposureresponse functions from observational data and then optimizes the objective via a greedy strategy. Our approach bridges causal inference with network optimization, providing provable guarantees for both the estimation of outcome functions and the approximation ratio of the influence maximization.
Paper Structure (35 sections, 17 theorems, 70 equations, 2 figures, 2 tables, 1 algorithm)

This paper contains 35 sections, 17 theorems, 70 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Framework and theoretical analysis
  4. Identification
  5. Estimation for a fixed seed set
  6. Optimization: from estimators to near-optimal seeding
  7. Experiments
  8. General Performance (RQ1)
  9. Robustness and Sensitivity (RQ2 & RQ3)
  10. Conclusion and Discussion
  11. Literature review
  12. Proofs for Section \ref{['sec:method']}
  13. Preliminaries: discrete concavity, interpolation, and curvature bounds
  14. Piecewise-linear extension.
  15. Proof of Proposition \ref{['prop:seedset-ips-id']} (seed-set IPS identification)
  16. ...and 20 more sections

Key Result

Proposition 3.2

Assume Assumption assump:replication. Define the weight $W_\ell(S):=\mathbb{I}(Z_\ell=S)/\pi_\ell(S\mid X_\ell).$ Then $F(S)$ is point identified by the observed law and satisfies $F(S)=\mathbb{E}[W_\ell(S)\cdot \sum_{i\in V}Y_{i\ell}].$ Moreover, the estimator $\widehat{F}_{\mathrm{IPS}}(S):=\frac{

Figures (2)

  • Figure 1: RQ2: Robustness analysis on GoodReads ($K=20$).
  • Figure 2: RQ3: Sensitivity to seed budget $K$.

Theorems & Definitions (35)

  • Proposition 3.2: Seed-set-level identification via IPS
  • Theorem 3.3: Structural reduction via exposure
  • Corollary 3.4: Second-order approximation of welfare
  • Theorem 3.5: Partial identification region for steady-state welfare
  • Theorem 3.6: Point identification via vanishing curvature or no multi-exposure coincidences
  • Theorem 3.7: Risk bound for shape-constrained exposure--response estimation
  • Lemma 3.8: Moment control for exposure increments under weak propagation
  • Proposition 3.9: Finite-sample concentration for exposure simulation
  • Theorem 3.10: Finite-sample error bound for steady-state welfare estimation (fixed $S$)
  • Theorem 3.11: Asymptotic identification and consistency (fixed $S$)
  • ...and 25 more