Causal Inference under Interference with Learned Exposure Mappings

Technical Summary: Causal Inference under Interference with Learned Exposure Mappings

Problem Statement
In causal inference under interference, the "exposure mapping" is a critical component that defines how treatments assigned to one unit affect the effective exposure of others. Traditional frameworks typically assume this mapping is known a priori, often specified via fixed geographic distances or network structures. However, in environmental applications—such as analyzing the health impacts of pollution control—the exposure mapping is not directly observed. Instead, it is induced by latent atmospheric transport processes that must be learned from pollution data.

This creates a fundamental challenge: while various transport models (mechanistic PDEs, physics-informed neural operators, Fourier neural operators, and foundation models) may achieve similar predictive accuracy in forecasting observed pollution concentrations, they may imply different underlying transport operators. Consequently, these models may generate distinct exposure mappings, leading to divergent causal conclusions regarding spillover effects. The paper investigates whether predictive agreement among transport models is sufficient for reliable causal inference when exposure mappings are learned rather than observed.

Methodology
The study employs a framework where a transport operator $T$ maps an intervention vector $A$ (emission reductions) to an exposure mapping $E(T) = TA$. The causal quantity of interest is the spillover effect on health outcomes $H$, modeled as a function of direct intervention and spillover exposure.

The author compares four distinct transport modeling approaches:

1. Mechanistic PDE: An advection–diffusion partial differential equation model.
2. PINO: Physics-Informed Neural Operators.
3. FNO: Fourier Neural Operators.
4. GeoPT: A recent foundation model for geophysical transport.

The evaluation proceeds in two stages:

• Simulation Study: A latent "true" transport operator $T^*$ generates pollution dynamics. Competing models are fitted to the resulting observed pollution field. The study assesses each model's ability to predict pollution ($PM$), recover the true exposure mapping, and estimate the true spillover effect.
• Empirical Analysis: The models are applied to California $PM_{2.5}$ data. The analysis examines how different transport assumptions affect inferred spillover patterns under hypothetical pollution-control interventions, without claiming to identify the single "true" atmospheric process.

Key Results

• Predictive Equivalence vs. Causal Divergence: In simulations, all four models achieved nearly identical pollution prediction accuracy ($R^2$ ranging from 0.970 to 0.975). However, their estimated spillover effects varied significantly, ranging from 1.78 to 2.27. The model that most accurately recovered the exposure mapping (FNO) produced the spillover estimate closest to the true value.
• Exposure Mapping Accuracy as a Predictor: The study found that accuracy in recovering the exposure mapping was a stronger predictor of inferential performance than marginal improvements in pollution prediction accuracy. Models with larger exposure mapping errors (e.g., PINO, GeoPT) produced larger deviations in spillover estimates.
• Intervention Sensitivity: The impact of exposure mapping uncertainty depended heavily on the intervention type:
  • Regional Interventions: Showed modest disagreement across models (spillover range: 1.79–2.42).
  • Upwind Interventions: Showed the smallest disagreement (range: 1.93–2.13).
  • Localized Point-Source Interventions: Showed substantial disagreement, with estimated spillover effects ranging from 0.51 (PDE) to 1.56 (GeoPT)—a three-fold difference.
• Empirical Findings (California): The analysis of California $PM_{2.5}$ data mirrored the simulation results. While competing models produced similar predictions of observed concentrations, they implied different spillover patterns and identified different locations as most affected by interventions. Notably, while spillover estimates varied, the overall estimated intervention effects remained stable (ranging from 0.303 to 0.305), suggesting that transport uncertainty impacts mechanistic understanding more than aggregate policy impact predictions.

Significance and Claims
The paper argues that predictive agreement alone is insufficient for reliable causal inference when exposure mappings are learned. The core contribution is demonstrating that models fitting observed data equally well can induce different exposure mappings, leading to substantially different conclusions about spillover effects, particularly for localized interventions.

The author claims that:

1. Exposure mappings should be treated as estimated quantities rather than fixed design objects, necessitating the propagation of uncertainty from the transport learning process into downstream causal analyses.
2. Evaluation criteria for transport models in causal settings must extend beyond predictive accuracy to include the stability and reliability of the induced exposure mappings.
3. Uncertainty in learned transport processes matters most for targeted interventions, where local transport behavior has a stronger influence on downstream exposure compared to broad regional interventions.

The study concludes that without accounting for the uncertainty in learned transport processes, causal inferences regarding spillover effects may be unreliable, even when the underlying models appear indistinguishable in terms of predictive performance.