揭示无需假设数据分布即可求解的统计问题边界
Distribution free M-estimation
- 通过凸M估计与随机优化框架，给出可无分布假设求解的充要条件
- 发现损失函数的利普希茨连续性并非无分布最小化必要条件
- 为统计学习理论提供新判据，适合理论研究者参考
长期以来，如何界定在不作任何底层数据分布假设的前提下可解的统计问题，一直是统计学和学习理论的核心议题。本文刻画了凸M估计或随机优化问题在无分布假设条件下可解的条件，明确划分了可解与不可解问题的界限。所识别的条件表明，被最小化的损失函数的利普希茨连续性并非无分布最小化的必要条件，且该条件与机器学习中经典的可学习性刻画有本质区别。
原文摘要 · Abstract (English)
The basic question of delineating those statistical problems that are solvable without making any assumptions on the underlying data distribution has long animated statistics and learning theory. This paper characterizes when a convex M-estimation or stochastic optimization problem is solvable in such an assumption-free setting, providing a precise dividing line between solvable and unsolvable problems. The conditions we identify show, perhaps surprisingly, that Lipschitz continuity of the loss being minimized is not necessary for distribution free minimization, and they are also distinct from classical characterizations of learnability in machine learning.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。