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. To estimate such semi-couplings and generalize out-of-sample, we derive an efficient parameterization based on neural optimal transport maps and propose a novel algorithmic scheme through a cycle-consistent training procedure. We apply our method to the challenging task of forecasting heterogeneous responses of multiple cancer cell lines to various drugs, where we observe that by accurately modeling cell proliferation and death, our method yields notable improvements over previous neural optimal transport methods.
翻译:在许多应用领域,测量人口具有破坏性,无法在同一样本中反复进行,例如在单细胞生物学中,最佳运输(OT)能够通过学习最佳地将分布的样本从未受重视的数据中最佳地混合在一起来应对这一挑战。然而,通常的OT的配方假定了质量保护,这在人口规模变化(如细胞扩散或死亡)测量之间的不平衡假设中是违反的。在这项工作中,我们采用了NubOT这一神经不平衡的OT配方,依赖半相联的正规主义来核算质量的创造和破坏。为了估计这种半相联和一般的配方,我们根据神经最优运输图进行高效的参数化,并通过循环协调的培训程序提出新的算法方案。我们采用我们的方法来预测多种癌症细胞线对各种药物的混杂反应,我们通过精确的细胞扩散和死亡模型观察到,我们的方法在以往的神经线上取得了显著的改进。