论文标题
在内存约束下，最佳的一通非参数估计
Optimal One-pass Nonparametric Estimation Under Memory Constraint
论文作者
论文摘要
对于流媒体设置中的非参数回归，数据不断流入并需要实时分析，主要挑战是，由于计算机内存和存储有限，一旦处理的计算机系统清除数据。我们通过提出一个基于刑罚的正交基础扩展并开发一个一般框架来研究统计效率和估计器记忆消耗之间的相互作用的一般框架来解决挑战。我们表明，在内存约束下，提出的估计器在统计上是最佳的，并且在所有相同估计质量的一通估计器中均无少量的记忆足迹。数值研究表明，所提出的一通估计器几乎与可以访问所有历史数据的非流媒体对应物一样有效。
For nonparametric regression in the streaming setting, where data constantly flow in and require real-time analysis, a main challenge is that data are cleared from the computer system once processed due to limited computer memory and storage. We tackle the challenge by proposing a novel one-pass estimator based on penalized orthogonal basis expansions and developing a general framework to study the interplay between statistical efficiency and memory consumption of estimators. We show that, the proposed estimator is statistically optimal under memory constraint, and has asymptotically minimal memory footprints among all one-pass estimators of the same estimation quality. Numerical studies demonstrate that the proposed one-pass estimator is nearly as efficient as its non-streaming counterpart that has access to all historical data.
