TL;DR
Standard optimal transport assumes mass is conserved—but cells die and proliferate. NubOT uses semi-couplings to model creation and destruction of mass, enabling accurate forecasting of how cancer cells respond to drugs.
Abstract
Comparing unpaired samples of a distribution or population taken at different points in time is a fundamental task in many application domains where measuring populations is destructive and cannot be done repeatedly on the same sample, such as in single-cell biology. Optimal transport (OT) can solve this challenge by learning an optimal coupling of samples across distributions from unpaired data. However, the usual formulation of OT assumes conservation of mass, which is violated in unbalanced scenarios in which the population size changes (e.g., cell proliferation or death) between measurements. In this work, we introduce NubOT, a neural unbalanced OT formulation that relies on the formalism of semi-couplings to account for creation and destruction of mass.
Citation
@article{lubeck2022neural,
title={Neural Unbalanced Optimal Transport via Cycle-Consistent Semi-Couplings},
author={L{\"u}beck, Frederike and Bunne, Charlotte and Gut, Gabriele and del Castillo, Jacobo Sarabia and Pelkmans, Lucas and Alvarez-Melis, David},
journal={arXiv preprint arXiv:2209.15621},
year={2022}
}