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Spatial Deconfounder: Interference-Aware Deconfounding for Spatial Causal Inference

Ayush Khot, Miruna Oprescu, Maresa Schröder, Ai Kagawa, Xihaier Luo

TL;DR

The paper tackles causal inference in spatial settings plagued by both interference and unobserved spatial confounding. It introduces the Spatial Deconfounder, a two-stage framework that first reconstructs a substitute latent confounder using a CVAE with a spatial prior from local and neighbor treatments, then uses a flexible outcome model to estimate direct and spillover effects. The authors prove identifiability of these effects under mild assumptions and demonstrate empirically that their method reduces bias relative to spatial baselines on extended SpaCE datasets drawn from environmental health and social science data. This approach reframes interference as a rich signal for uncovering hidden structure, enabling robust causal estimates in structured spatial systems with limited observability. The work bridges spatial causal inference, deconfounding, and deep latent-variable modeling, and outlines avenues for extending to spatiotemporal data and continuous treatments.

Abstract

Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: interference reveals structure in the latent confounder. Leveraging this insight, we propose the Spatial Deconfounder, a two-stage method that reconstructs a substitute confounder from local treatment vectors using a conditional variational autoencoder (CVAE) with a spatial prior, then estimates causal effects via a flexible outcome model. We show that this approach enables nonparametric identification of both direct and spillover effects under weak assumptions--without requiring multiple treatment types or a known model of the latent field. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world datasets in environmental health and social science. By turning interference into a multi-cause signal, our framework bridges spatial and deconfounding literatures to advance robust causal inference in structured data.

Spatial Deconfounder: Interference-Aware Deconfounding for Spatial Causal Inference

TL;DR

The paper tackles causal inference in spatial settings plagued by both interference and unobserved spatial confounding. It introduces the Spatial Deconfounder, a two-stage framework that first reconstructs a substitute latent confounder using a CVAE with a spatial prior from local and neighbor treatments, then uses a flexible outcome model to estimate direct and spillover effects. The authors prove identifiability of these effects under mild assumptions and demonstrate empirically that their method reduces bias relative to spatial baselines on extended SpaCE datasets drawn from environmental health and social science data. This approach reframes interference as a rich signal for uncovering hidden structure, enabling robust causal estimates in structured spatial systems with limited observability. The work bridges spatial causal inference, deconfounding, and deep latent-variable modeling, and outlines avenues for extending to spatiotemporal data and continuous treatments.

Abstract

Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: interference reveals structure in the latent confounder. Leveraging this insight, we propose the Spatial Deconfounder, a two-stage method that reconstructs a substitute confounder from local treatment vectors using a conditional variational autoencoder (CVAE) with a spatial prior, then estimates causal effects via a flexible outcome model. We show that this approach enables nonparametric identification of both direct and spillover effects under weak assumptions--without requiring multiple treatment types or a known model of the latent field. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world datasets in environmental health and social science. By turning interference into a multi-cause signal, our framework bridges spatial and deconfounding literatures to advance robust causal inference in structured data.

Paper Structure

This paper contains 26 sections, 3 theorems, 37 equations, 3 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background and Setup
  4. Methodology
  5. Theoretical Properties of the Spatial Deconfounder
  6. Experiments
  7. Conclusion
  8. Acknowledgments
  9. Extended Literature Review
  10. Spatial Causal Inference Under Interference and Spatially Structured Confounding
  11. Classical spatial causal inference.
  12. Spatial confounding and bias-adjustment methods.
  13. Deconfounding Methods for ATE Estimation with Unobserved Confounders
  14. Deep Learning for Spatial and Latent Structure Modeling
  15. Deep learning for spatial modeling.
  16. ...and 11 more sections

Key Result

Theorem 1

Suppose Assumptions assump:consistency–assump:conditional_consistency_confounder hold. Let $Z$ be a piecewise constant function of the assigned causes and covariates $(a,\mathbf a_{{\mathcal{N}}},{\bm{x}},{\bm{x}}_{{\mathcal{N}}})$ and let the outcome be a separable function of the observed and unob for continuously differentiable functions $f_1,f_2,f_3,f_4$. Consequently, the direct and spillover

Figures (3)

  • Figure 1: Schematic of spatial interference/confounding. Spatial data is represented in geographical cells indexed by site $s$ with neighborhood $\mathcal{N}_s$. The outcome at $s$ (e.g., mortality rate) is affected by the treatments (e.g., air quality) and observed confounders (e.g., demographic informataion) at both $s$ and $\mathcal{N}_s$. However, unobserved latent factors (e.g., humidity) can confound the relationship, rendering causal effects unidentifiable.
  • Figure 2: Example spatial distribution of (normalized) confounder, treatment, and outcome in real-world dataset. The confounder $U(s)$ (summer humidity) varies smoothly across space, while the treatment $A_s$ (PM$_{2.5}$) shows more local heterogeneity. The outcome $Y_s$ (respiratory and cardiovascular mortality) reflects broader spatial health patterns.
  • Figure 3: Architecture of the spatial deconfounder & estimation framework. Stage : The CVAE takes treatments and observed confounders as input to learn the latent substitute confounder. Stage : We employ the reconstructed confounder together with the observed variables (now including the outcome) to train the potential outcome estimation module.

Theorems & Definitions (9)

  • Remark 1: End-to-end variant
  • Theorem 1: Causal identifiability
  • proof
  • Definition 1: Ignorability
  • Definition 2: Factor models
  • Lemma 1
  • proof
  • Theorem 1: Causal identifiability
  • proof