Deep Causal Inference for Point-referenced Spatial Data with Continuous Treatments

TL;DR

This work tackles causal inference for point-referenced spatial data with multiple continuous treatments by integrating neural networks with an approximate Gaussian process to capture nonlinear spatial interference and unobserved confounding. The core model separates a linear direct effect from nonlinear indirect effects modeled by CNN/ U‑Net architectures, while U contributes via an Implicit Composite Kernel-based GP approximation. To handle partially observed outcomes, the authors employ generalized propensity-score balancing, kernel-density estimates, and self-normalization in estimating DE, IE, and TE. Across synthetic, semi-synthetic, and real-world satellite-imagery data, NN-based spatial causal inference outperforms linear baselines in estimating causal effects and yields more plausible, actionable predictions for environmental applications such as urban heat island studies.

Abstract

Causal reasoning is often challenging with spatial data, particularly when handling high-dimensional inputs. To address this, we propose a neural network (NN) based framework integrated with an approximate Gaussian process to manage spatial interference and unobserved confounding. Additionally, we adopt a generalized propensity-score-based approach to address partially observed outcomes when estimating causal effects with continuous treatments. We evaluate our framework using synthetic, semi-synthetic, and real-world data inferred from satellite imagery. Our results demonstrate that NN-based models significantly outperform linear spatial regression models in estimating causal effects. Furthermore, in real-world case studies, NN-based models offer more reasonable predictions of causal effects, facilitating decision-making in relevant applications.

Figures (4)

• Figure 1: Causal relationships among the treatment $T$, the outcome $Y$, and the observed confounder $X$ (with $U$ excluded) under the assumptions of (a) no interference and (b) local interference where the neighboring area $\mathcal{S}$ only covers the immediate neighbors of each unit. Here we show a simplified 1-dimensional example with neighborhood window of size 1, although the spatial problem is 2-dimensional and neighborhood window is larger in the work presented here.
• Figure 2: Geospatial datasets used for semi-synthetic and real-world experiments. Land cover classes are provided in Appendix \ref{['appx:B']}
• Figure 3: Distribution of the indirect effect on temperature from NDVI for both linear and NN-based models, where the bar shows the $25^{th}$, $50^{th}$ (i.e., median), and $75^{th}$ percentiles while the whiskers extend to show the rest of the distribution. Bars to the left of the blue dashed line represent land cover types with high building intensity, while those to the right represent land cover types with low building intensity.
• Figure 4: Visualization of the direct and indirect effects from NDVI and albedo on the surface air temperature in the downtown region of Durham.