论文标题
预算受限的界限用于最佳运输的迷你批量估算
Budget-Constrained Bounds for Mini-Batch Estimation of Optimal Transport
论文作者
论文摘要
最佳传输（OT）是比较概率分布的基本工具，但其确切的计算对于大型数据集仍然过于刺激。在这项工作中，我们介绍了上限和下限的新型家族，以通过汇总Mini批次OT问题的解决方案构成的OT问题。上界的家庭包含一个极端的传统迷你批量平均，并且通过在另一个极端的最佳耦合中发现了紧密的界限。在这些极端之间，我们提出了各种方法来基于固定的计算预算构建界限。通过各种实验，我们探讨了计算预算与界限紧密度之间的权衡，并显示了这些界限在计算机视觉应用中的有用性。
Optimal Transport (OT) is a fundamental tool for comparing probability distributions, but its exact computation remains prohibitive for large datasets. In this work, we introduce novel families of upper and lower bounds for the OT problem constructed by aggregating solutions of mini-batch OT problems. The upper bound family contains traditional mini-batch averaging at one extreme and a tight bound found by optimal coupling of mini-batches at the other. In between these extremes, we propose various methods to construct bounds based on a fixed computational budget. Through various experiments, we explore the trade-off between computational budget and bound tightness and show the usefulness of these bounds in computer vision applications.
