论文标题
神经最佳运输具有一般成本功能
Neural Optimal Transport with General Cost Functionals
论文作者
论文摘要
我们引入了一种新型的基于神经网络的算法，以计算一般成本功能的最佳运输计划（OT）计划。与普通的欧几里得成本相比，即$ \ ell^1 $或$ \ ell^2 $，此类功能提供了更大的灵活性，并允许使用辅助信息（例如类标签）来构建所需的传输图。现有的一般成本方法是离散的，在实践中有局限性，即它们不提供样本外估计。我们应对设计一种连续的OT方法的挑战，用于一般成本，该方法将高维空间（例如图像）中的新数据点推广到新的数据点。此外，我们为回收的运输计划提供理论错误分析。作为一个应用程序，我们在保留班级结构的同时构建了映射数据分布的成本功能。
We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., $\ell^1$ or $\ell^2$, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.
