A Robust Local Fr\'echet Regression Using Unbalanced Neural Optimal Transport with Applications to Dynamic Single-cell Genomics Data

Single-cell RNA sequencing (scRNA-seq) technologies have enabled the profiling of gene expression for a collection of cells across time during a dynamic biological process. Given that each time point provides only a static snapshot, modeling and understanding the underlying cellular dynamics remains a central yet challenging task in modern genomics. To associate biological time with single cell distributions, we develop a robust local Fr\'echet regression for interpolating the high-dimensional cellular distribution at any given time point using data observed over a finite time points. To allow for robustness in cell distributions, we propose to apply the unbalanced optimal transport-based Wasserstein distance in our local Fr\'echet regression analysis. We develop a computationally efficient algorithm to generate the cell distribution for a given time point using generative neural networks. The resulting single cell generated models and the corresponding transport plans can be use to interpolate the single cells at any unobserved time point and to track the cell trajectory during the cell differentiation process. We demonstrate the methods using three single cell differentiation data sets, including differentiation of human embryonic stem cells into embryoids, mouse hematopoietic and progenitor cell differentiation, and reprogramming of mouse embryonic fibroblasts. We show that the proposed methods lead to better single cell interpolations, reveal different cell differential trajectories, and identify early genes that regulate these cell trajectories.