Sparse Principal Component Analysis via Wavelets for Distributed Data

研究问题: 摘要称，研究如何在数据分散于多台机器、无法直接访问全样本的分布式（联邦学习）场景下，把高维情形下基于小波的稀疏化与变量选择引入分布式主成分分析，以在降低通信成本的同时保持特征子空间估计质量。
方法与思路: 作者提出将 Johnstone & Lu (2009) 的小波稀疏化方法嵌入 Fan et al. (2019) 的分布式 PCA 框架，在分布式计算中只传递被选中的稀疏系数；并通过 d 从 52 到 5000 的模拟比较所提方法与 Fan et al. (2019) 的估计误差与传输系数数量。
材料陈述的贡献: 摘要称，模拟结果显示在超过某一维度阈值后（λ=25 时 d≥152，λ=50 时 d≥252），所提方法在估计误差上优于 Fan et al. (2019)，且在整个研究范围内传输的系数数量系统性更少，从而在不损害特征子空间估计质量的前提下降低通信成本。
阅读关注点: 阅读全文时应核对：小波稀疏化的具体识别与阈值规则、分布式聚合与通信协议细节、误差度量与模拟设计、阈值维度结论对 λ 与数据生成设定的敏感性，以及是否给出理论保证或仅依赖模拟。
阅读边界: 摘要未说明理论性质、真实数据应用与渐近结果，模拟结论不能外推为普遍优势；该文为 arXiv 预印本，未经同行评审或期刊接收验证，且摘要提及的资助信息不构成质量证据。

DeepSeek Flash · 2026-10-11

原文摘要

The large volume of data and concerns about data privacy have motivated the development of techniques for distributed data, a problem also known as federated learning. In this scenario, sub-samples of the data are divided across different machines, and statistics must be computed over that data without direct access to the full sample. Johnstone & Lu (2009, JASA) show that principal component analysis (PCA) is statistically inconsistent in the high-dimensional regime, and propose a way to recover consistency through wavelet-based sparsification and variable selection. Fan et al. (2019, AoS) show a way to perform this same estimation -- specifically, to estimate the eigenspace that would be obtained if all the data were pooled together, even though it remains effectively distributed -- without addressing the high-dimensional regime. This work incorporates the wavelet-based sparsification of Johnstone & Lu (2009) into the distributed PCA framework of Fan et al. (2019), aiming to reduce communication cost without compromising the quality of the eigenspace estimation. Simulations across $d \in [52, 5000]$ show that the proposed method overtakes Fan et al. (2019) in estimation error beyond a clear dimensional threshold ( $d \geq 152$ for $λ=25$ , $d \geq 252$ for $λ=50$ ), while transmitting systematically fewer coefficients throughout the entire range studied. This study was financed by the Sao Paulo Research Foundation (FAPESP), Brazil. Process Number #2023/02538-0 and Number #2025/21250-2.The large volume of data and concerns about data privacy have motivated the development of techniques for distributed data, a problem also known as federated learning. In this scenario, sub-samples of the data are divided across different machines, and statistics must be computed over that data without direct access to the full sample. Johnstone & Lu (2009, JASA) show that principal component analysis (PCA) is statistically inconsistent in the high-dimensional regime, and propose a way to recover consistency through wavelet-based sparsification and variable selection. Fan et al. (2019, AoS) show a way to perform this same estimation -- specifically, to estimate the eigenspace that would be obtained if all the data were pooled together, even though it remains effectively distributed -- without addressing the high-dimensional regime. This work incorporates the wavelet-based sparsification of Johnstone & Lu (2009) into the distributed PCA framework of Fan et al. (2019), aiming to reduce communication cost without compromising the quality of the eigenspace estimation. Simulations across $d \in [52, 5000]$ show that the proposed method overtakes Fan et al. (2019) in estimation error beyond a clear dimensional threshold ($d \geq 152$ for $λ=25$, $d \geq 252$ for $λ=50$), while transmitting systematically fewer coefficients throughout the entire range studied. This study was financed by the Sao Paulo Research Foundation (FAPESP), Brazil. Process Number #2023/02538-0 and Number #2025/21250-2.

摘要来源：arXiv

笔记与分组

分类依据与纠错

Sparse Principal Component Analysis via Wavelets for Distributed Data

作者的期刊发表依据

代码、数据与补充材料

基于小波的分布式数据稀疏主成分分析

原文摘要

同方向的基础文献

同方向的基础文献