# 基于核的最优传输估计器专用半光滑牛顿法

- 来源：Apple Machine Learning Research（RSS）
- 发布时间：2026-08-18 08:00
- AIHOT 分数：43
- AIHOT 链接：https://aihot.virxact.com/items/cmszdue520amprodpg9bukr8l
- 原文链接：https://machinelearning.apple.com/research/semismooth-newton-optimal-transport

## AI 摘要

苹果机器学习研究团队提出一种专用半光滑牛顿法，用于加速基于核的最优传输（OT）估计器的计算。该方法替代了此前依赖短步内点法（SSIPM）的求解路径，后者在实际中迭代次数庞大、计算代价高昂。新方法在保持高维概率分布比较中统计效率优势的同时，显著降低计算开销。

## 正文

Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. Recent works suggest that these estimators are more statistically efficient than plug-in (linear programming-based) OT estimators when comparing probability measures in high-dimensions [Vacher et al., 2021]. Unfortunately, that statistical benefit comes at a very steep computational price: because their computation relies on the short-step interior-point method (SSIPM), which comes with a large iteration count in practice, these estimators quickly become…