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

TL;DR

This paper introduces a robust local Fréchet regression method utilizing unbalanced neural optimal transport to interpolate and analyze high-dimensional single-cell gene expression data over time, revealing cellular trajectories and key regulatory genes.

Contribution

It develops a novel robust regression framework with neural optimal transport for dynamic single-cell data analysis, improving interpolation and trajectory inference.

Findings

Enhanced cell distribution interpolation accuracy

Revealed distinct cell differentiation trajectories

Identified early regulatory genes in cell development

Abstract

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.