q-Diffusion leverages the full dimensionality of gene coexpression in single-cell transcriptomics

Unlocking the full dimensionality of single-cell RNA sequencing data (scRNAseq) is the next frontier to a richer, fuller understanding of cell biology. We introduce q-diffusion, a framework for capturing the coexpression structure of an entire library of genes, improving on state-of-the-art analysis tools. The method is demonstrated via three case studies. In the first, q-diffusion helps gain statistical significance for differential effects on patient outcomes when analyzing the CALGB/SWOG 80405 randomized phase III clinical trial, suggesting precision guidance for the treatment of metastatic colorectal cancer. Secondly, q-diffusion is benchmarked against existing scRNAseq classification methods using an in vitro PBMC dataset, in which the proposed method discriminates IFN-γ stimulation more accurately. The same case study demonstrates improvements in unsupervised cell clustering with the recent Tabula Sapiens human atlas. Finally, a local distributional segmentation approach for spatial scRNAseq, driven by q-diffusion, yields interpretable structures of human cortical tissue.

A Metric Space for Point Process Excitations

A multivariate Hawkes process enables self- and cross-excitations through a triggering matrix that behaves like an asymmetrical covariance structure, characterizing pairwise interactions between the event types. Full-rank estimation of all interactions is often infeasible in empirical settings. Models that specialize on a spatiotemporal application alleviate this obstacle by exploiting spatial locality, allowing the dyadic relationships between events to depend only on separation in time and relative distances in real Euclidean space. Here we generalize this framework to any multivariate Hawkes process, and harness it as a vessel for embedding arbitrary event types in a hidden metric space. Specifically, we propose a Hidden Hawkes Geometry (HHG) model to uncover the hidden geometry between event excitations in a multivariate point process. The low dimensionality of the embedding regularizes the structure of the inferred interactions. We develop a number of estimators and validate the model by conducting several experiments. In particular, we investigate regional infectivity dynamics of COVID-19 in an early South Korean record and recent Los Angeles confirmed cases. By additionally performing synthetic experiments on short records as well as explorations into options markets and the Ebola epidemic, we demonstrate that learning the embedding alongside a point process uncovers salient interactions in a broad range of applications.