CDS: Counterfactual Directionality Score for Structured Interventions in Spatial Graphs

2026-07-15

AI Summary

Existing methods struggle to quantify directed influences among cell types in spatial graphs under controlled perturbations. This work proposes a structured counterfactual intervention framework that integrates a Neighborhood Influence Model (NIM) with constrained neighborhood perturbations to estimate directional effects while preserving spatial structure. The approach introduces a Counterfactual Directionality Score (CDS)—a finite-difference measure of local intervention sensitivity—and employs a core-level bootstrap procedure to properly calibrate uncertainty under spatial dependence. Evaluated on synthetic data, the method accurately recovers known directional influences, maintains well-calibrated type I error control under the null hypothesis, and demonstrates robustness to confounding factors. Applied to spatial transcriptomics datasets, it reveals biologically plausible and cross-tissue consistent patterns of cellular interactions.

Abstract

Quantifying directional influence between node populations is a fundamental problem in graph-based modeling, particularly in spatial biological systems where cell-cell interactions shape functional outcomes. Existing approaches based on attention, attribution, or correlation capture associations but do not provide a principled framework for evaluating directional effects under controlled perturbations. We introduce a framework for structured counterfactual interventions in graph-based models to estimate directional influence between node types. Our approach trains a Neighbor Influence Model (NIM) to predict node states from local neighborhoods and applies constrained interventions that modify neighborhood composition while preserving key spatial and structural properties. We define the Counterfactual Directionality Score (CDS), which measures the change in predicted node state induced by targeted perturbations, and provide a theoretical interpretation of CDS as a finite-difference measure of local intervention sensitivity. To obtain valid uncertainty estimates, we introduce a core-level bootstrap procedure that accounts for dependencies within spatial samples. Experiments on synthetic spatial graphs with known directional structure show that CDS recovers directional influence, remains well calibrated under null conditions, and is robust to confounding signals, while preliminary results on spatial transcriptomics data reveal biologically plausible and consistent interactions across tissue cores.

Problem

• directional influence
• spatial graphs
• counterfactual interventions
• graph-based modeling
• structured perturbations

Innovation

• Counterfactual Directionality Score
• Structured Interventions
• Spatial Graphs
• Neighbor Influence Model
• Bootstrap Uncertainty