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Estimating Direct and Indirect Causal Effects of Spatiotemporal Interventions in Presence of Spatial Interference

Sahara Ali, Omar Faruque, Jianwu Wang

TL;DR

This paper formalizes the concept of spatial interference in case of time-varying treatment assignments by extending the potential outcome framework under the assumption of no unmeasured confounding, and proposes a deep learning based potential outcome model for spatiotemporal causal inference.

Abstract

Spatial interference (SI) occurs when the treatment at one location affects the outcomes at other locations. Accounting for spatial interference in spatiotemporal settings poses further challenges as interference violates the stable unit treatment value assumption, making it infeasible for standard causal inference methods to quantify the effects of time-varying treatment at spatially varying outcomes. In this paper, we first formalize the concept of spatial interference in case of time-varying treatment assignments by extending the potential outcome framework under the assumption of no unmeasured confounding. We then propose our deep learning based potential outcome model for spatiotemporal causal inference. We utilize latent factor modeling to reduce the bias due to time-varying confounding while leveraging the power of U-Net architecture to capture global and local spatial interference in data over time. Our causal estimators are an extension of average treatment effect (ATE) for estimating direct (DATE) and indirect effects (IATE) of spatial interference on treated and untreated data. Being the first of its kind deep learning based spatiotemporal causal inference technique, our approach shows advantages over several baseline methods based on the experiment results on two synthetic datasets, with and without spatial interference. Our results on real-world climate dataset also align with domain knowledge, further demonstrating the effectiveness of our proposed method.

Estimating Direct and Indirect Causal Effects of Spatiotemporal Interventions in Presence of Spatial Interference

TL;DR

This paper formalizes the concept of spatial interference in case of time-varying treatment assignments by extending the potential outcome framework under the assumption of no unmeasured confounding, and proposes a deep learning based potential outcome model for spatiotemporal causal inference.

Abstract

Spatial interference (SI) occurs when the treatment at one location affects the outcomes at other locations. Accounting for spatial interference in spatiotemporal settings poses further challenges as interference violates the stable unit treatment value assumption, making it infeasible for standard causal inference methods to quantify the effects of time-varying treatment at spatially varying outcomes. In this paper, we first formalize the concept of spatial interference in case of time-varying treatment assignments by extending the potential outcome framework under the assumption of no unmeasured confounding. We then propose our deep learning based potential outcome model for spatiotemporal causal inference. We utilize latent factor modeling to reduce the bias due to time-varying confounding while leveraging the power of U-Net architecture to capture global and local spatial interference in data over time. Our causal estimators are an extension of average treatment effect (ATE) for estimating direct (DATE) and indirect effects (IATE) of spatial interference on treated and untreated data. Being the first of its kind deep learning based spatiotemporal causal inference technique, our approach shows advantages over several baseline methods based on the experiment results on two synthetic datasets, with and without spatial interference. Our results on real-world climate dataset also align with domain knowledge, further demonstrating the effectiveness of our proposed method.
Paper Structure (17 sections, 10 equations, 5 figures, 1 table)

This paper contains 17 sections, 10 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations and Definitions
  4. Assumptions
  5. Spatio-Temporal Causal Inference Network (STCINet)
  6. Latent Factor Model for Temporal Confounding
  7. Double Attention Mechanism
  8. U-Net for Spatial Interference
  9. Experiments
  10. Synthetic Dataset
  11. Evaluation Metrics
  12. Experimental Setup
  13. Ablation Study
  14. Comparison with Baseline Methods
  15. Case Study on Real-World Arctic Data
  16. ...and 2 more sections

Figures (5)

  • Figure 1: Different scenarios of causation (black), confounding (blue) and interference (red) in spatiotemporal data. (a) No confounding, no interference, only temporal causation; (b) No interference, only temporal confounding and temporal causation; (c) No temporal confounding, only spatial interference and temporal causation; (d) Temporal confounding, spatial interference, temporal causation.
  • Figure 2: Overall architecture of proposed spatiotemporal causal inference network (STCINet).
  • Figure 3: Sub-modules of STCINet: (a) Attention gating mechanism to identify patterns of spatial interference, (b) Latent factor model for deconfounding covariate and treatment history.
  • Figure 4: Potential outcome variable $Y$ at timesteps 10, 100, 1000, 2000 and 4000. Top row: Outcome under no intervention at different timesteps. Middle row: Intervened outcome at different timesteps. Bottom row: Spillover effects at different timesteps, which is the difference in intervened outcomes with and without the spatial interference.
  • Figure 5: Case study on climate data when longwave radiations are reduced by 5%. (a) Region of applying treatment, (b) Lagged Average treatment effect (LATE) on Summer SIC for 1979-2021, (c) LATE on Summer SIC for 1990, (d) LATE on Summer SIC for 2003.