Nonparametric kernel-based detection of spatially variable genes with adaptive shrinkage and scalable multi-sample inference

<jats:p>Identifying spatially variable genes (SVGs), genes whose expression varies coherently across tissue space, is a central analytic goal in spatially resolved transcriptomics. Current methods rank spatially variable genes using either significance probabilities from parametric models or effect sizes such as the proportion of spatial variance, but parametric approaches impose distributional assumptions, such as Gaussian processes or negative binomial models, that may be violated for sparse or zero-inflated data. Furthermore, most detection tools cannot jointly model multiple biological replicates, and no existing framework provides both nonparametric significance probabilities and stabilized effect-size estimates with formal uncertainty quantification. Here, we introduce CytoKspace, a nonparametric framework that combines a sparse exponential kernel constructed from nearest-neighbor graphs with a quadratic-form test statistic and adaptive permutation testing. CytoKspace employs a multi-stage adaptive permutation schedule that yields substantial computational savings over fixed-permutation baselines, an adaptive shrinkage layer built on empirical Bayes estimation that stabilizes raw spatial effect sizes and provides posterior estimates with local false sign rates, and a scalable multi-sample extension via Fisher combination of significance probabilities and inverse-variance-weighted meta-analysis that accommodates studies with multiple biological replicates. In extensive simulations across a broad range of sample sizes, gene counts, spatially variable gene fractions, and effect sizes, as well as in applications to two real datasets from the Visium and seqFISH platforms, CytoKspace demonstrates competitive sensitivity, well-calibrated false positive rates, and practical computational requirements compared to existing methods. A software implementation of our method is freely available at \url{https://github.com/Ghoshlab/CytoKspace}.</jats:p>