Di Su | Searcharxiv

arXiv2026

Detecting change regions on spheres

While change point detection in time series data has been extensively studied, little attention has been given to its generalisation to data observed on spheres or other manifolds, where changes may occur within spatially complex regions with irregular boundaries, posing significant challenges. We propose a new class of estimators, namely, Change Region Identification and SeParation (CRISP), to locate changes in the mean function of a signal-plus-noise model defined on $d$-dimensional spheres. The CRISP estimator applies to scenarios with a single change region, and is extended to multiple change regions via a newly developed generic scheme. The convergence rate of the CRISP estimator is shown to depend on the VC dimension of the hypothesis class that characterises the change regions in general. We also carefully study the case where change regions have the geometry of spherical caps. Simulations confirm the promising finite-sample performance of this approach. The CRISP estimator's practical applicability is further demonstrated through two real data sets on global temperature and ozone hole.

stat.ME↗

arXiv2026

A New Framework for Explainable Rare Cell Identification in Single-Cell Transcriptomics Data

The detection of rare cell types in single-cell transcriptomics data is crucial for elucidating disease pathogenesis and tissue development dynamics. However, a critical gap that persists in current methods is their inability to provide an explanation based on genes for each cell they have detected as rare. We identify three primary sources of this deficiency. First, the anomaly detectors often function as "black boxes", designed to detect anomalies but unable to explain why a cell is anomalous. Second, the standard analytical framework hinders interpretability by relying on dimensionality reduction techniques, such as Principal Component Analysis (PCA), which transform meaningful gene expression data into abstract, uninterpretable features. Finally, existing explanation algorithms cannot be readily applied to this domain, as single-cell data is characterized by high dimensionality, noise, and substantial sparsity. To overcome these limitations, we introduce a framework for explainable anomaly detection in single-cell transcriptomics data which not only identifies individual anomalies, but also provides a visual explanation based on genes that makes an instance anomalous. This framework has two key ingredients that are not existed in current methods applied in this domain. First, it eliminates the PCA step which is deemed to be an essential component in previous studies. Second, it employs the state-of-art anomaly detector and explainer as the efficient and effective means to find each rare cell and the relevant gene subspace in order to provide explanations for each rare cell as well as the typical normal cell associated with the rare cell's closest normal cells.

q-bio.GN↗