CDS: Counterfactual Directionality Score for Structured Interventions in Spatial Graphs

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.

hSNMF: Hybrid Spatially Regularized NMF for Image-Derived Spatial Transcriptomics

High-resolution spatial transcriptomics platforms, such as Xenium, generate single-cell images that capture both molecular and spatial context, but their extremely high dimensionality poses major challenges for representation learning and clustering. In this study, we analyze data from the Xenium platform, which captures high-resolution images of tumor microarray (TMA) tissues and converts them into cell-by-gene matrices suitable for computational analysis. We benchmark and extend nonnegative matrix factorization (NMF) for spatial transcriptomics by introducing two spatially regularized variants. First, we propose Spatial NMF (SNMF), a lightweight baseline that enforces local spatial smoothness by diffusing each cell's NMF factor vector over its spatial neighborhood. Second, we introduce Hybrid Spatial NMF (hSNMF), which performs spatially regularized NMF followed by Leiden clustering on a hybrid adjacency that integrates spatial proximity (via a contact-radius graph) and transcriptomic similarity through a tunable mixing parameter alpha. Evaluated on a cholangiocarcinoma dataset, SNMF and hSNMF achieve markedly improved spatial compactness (CHAOS < 0.004, Moran's I > 0.96), greater cluster separability (Silhouette > 0.12, DBI < 1.8), and higher biological coherence (CMC and enrichment) compared to other spatial baselines. Availability and implementation: https://github.com/ishtyaqmahmud/hSNMF