Spatially aware empirical Bayes matrix factorization with applications to spatial transcriptomics

Faculty Mentor: Matthew Stephens (University of Chicago)

Obtaining a comprehensive spatiomolecular view of transcription and related biological processes is essential for under-standing tissue, cellular function and disease pathology. Driven by this need, large investments have been made in spatial transcriptomic technologies. These technologies have rapidly improved and expanded over the last decade, the latest of which can profile millions of cells in many tissues at high spatial resolution. These developments offer the potential to make progress in understanding biology of disease, but they also bring new analysis challenges. Therefore, there is an urgent need for new analysis tools that can extract insights from these complex, large-scale data sets in a way that is readily interpretable by researchers. We propose to meet this aim by developing new mathematical and statistical tools for spatial transcriptomics data. In particular, we propose a novel unsupervised modeling framework, “spatially aware” empirical Bayes matrix factorization (EBMF), that balances computational scalability and modeling flexibility. By integrating a broad family of Gaussian process (GP)-based priors into EBMF, the proposed modeling framework will help achieve the promise of spatial transcriptomics to uncover and characterize latent spatial gene expression programs with diverse properties. The new framework addresses the limitations of existing methods for these data while maintaining scalable computation and a modular, extensible architecture that allows modeling choices to adapt to different technologies and different experiment designs. Ultimately, our new methods will unite mathematics with biology, providing powerful mathematical tools that will enable biologists to gain new insights into spatially resolved molecular mechanisms and biological processes.