(proba-stats) Kernel-based perturbation testing for single-cell data

Advances in single-cell sequencing have enabled high-dimensional profiling of individual cells, giving rise to single-cell data science and new statistical challenges. A key task is the comparative analysis of single-cell datasets across conditions, tissues, or perturbations, where traditional gene-wise differential expression methods often fail to capture complex, non-linear distributional differences. Perturbation experiments further amplify this challenge by introducing structured, high-dimensional responses that are poorly modeled by linear approaches.

We propose a kernel-based framework for differential analysis of single-cell data that enables non-linear, distribution-level comparisons by embedding data into a reproducing kernel Hilbert space. Our method quantifies differences between cellular populations through distances between mean embeddings and supports formal hypothesis testing in complex experimental designs, including perturbation studies via linear models in RKHS. The approach is robust to high dimensionality, sparsity, and noise, and is implemented in the Python package kaov, which provides visualization and interpretation tools. By offering a flexible, distribution-free alternative to classical methods, kernel-based testing facilitates the detection of subtle but biologically meaningful changes in single-cell data, enabling deeper insights into cellular regulation, disease mechanisms, and precision medicine.