Zitian Wu | Searcharxiv

arXiv2026

Sparse Reduced-rank Regression Methods for Spatially Misaligned Data with Application to Spatial Transcriptomics

Understanding the spatiotemporal dynamics of disease progression in relation to transcriptomic profiles provides key insights into complex conditions such as Alzheimer's disease. To enable such investigations, STARmap PLUS technology offers joint profiling of high-resolution spatial transcriptomics and protein detection within the same tissue section. Detailed visual and clustering-based analyses of STARmap PLUS data by Zeng et al. (2023) provided important insights into molecular and cellular changes associated with Alzheimer's disease pathology. Motivated by this work, we develop a kernel-weighted sparse reduced-rank regression framework that estimates associations between plaque size and neighboring cell-level transcriptomic profiles while enabling gene selection and borrowing strength across genes, cell types, and disease stages. The proposed approach is implemented in a fully automated manner with data-driven specification of key model components. Through simulation studies, we demonstrate the robustness of the proposed method and its superiority across a range of simulation scenarios. Applied to Alzheimer's disease data, the proposed framework uncovers biologically meaningful associations, highlighting its potential for advancing the understanding of disease mechanisms.

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arXiv2025

Graphical Model-based Inference on Persistent Homology

Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use across domains such as computer vision and neuroscience. Most statistical treatments, however, use homology primarily as a feature extractor, relying on statistical distance-based tests or simple time-to-event models for inferential tasks. While these approaches can detect global differences, they rarely localize the source of those differences. We address this gap by taking a graphical model-based approach: we associate each vertex with a population latent position in a conic space and model each bar's key events (birth and death times) using an exponential distribution, whose rate is a transformation of the latent positions according to an event occurring on the graph. The low-dimensional bars have simple graph-event representations, such as the formation of a minimum spanning tree or the triangulation of a loop, and thus enjoy tractable likelihoods. Taking a Bayesian approach, we infer latent positions and enable model extensions such as hierarchical models that allow borrowing strength across groups. Applications to a neuroimaging study of Alzheimer's disease demonstrate that our method localizes sources of difference and provides interpretable, model-based analyses of topological structure in complex data. The code is provided and maintained at https://github.com/zitian-wu/graphPH.

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