标题： 可证明的模型并行分布式主成分分析与并行去噪 显示英文标题

标题： Provable Model-Parallel Distributed Principal Component Analysis with Parallel Deflation

摘要： 我们研究了一个分布式主成分分析（PCA）框架，其中每个工作者针对一个不同的特征向量，并通过从被认为“更优”的同伴提供的中间解进行更新来优化其解决方案。 从集中式特征值问题中的降秩方法中获得启发，我们的方法打破了降秩步骤中的顺序依赖性，允许工作者异步更新，同时仅产生较小的通信成本。 据我们所知，文献中存在一个空白——即这种分布式、动态的工作者之间相互作用的理论基础——仍未被解决。 本文提供了一个理论分析，解释了为什么、如何以及在什么情况下这些中间的分层更新能够在分布式环境中实现实际且可证明的收敛。 尽管这是一项理论工作，但我们的原型实现表明，这种分布式PCA算法能够有效且可扩展地收敛：通过实验，我们提出的框架在性能上与EigenGame-$\mu$相当，后者是当前最先进的模型并行PCA求解器。 显示英文摘要

摘要： We study a distributed Principal Component Analysis (PCA) framework where each worker targets a distinct eigenvector and refines its solution by updating from intermediate solutions provided by peers deemed as "superior". Drawing intuition from the deflation method in centralized eigenvalue problems, our approach breaks the sequential dependency in the deflation steps and allows asynchronous updates of workers, while incurring only a small communication cost. To our knowledge, a gap in the literature -- the theoretical underpinning of such distributed, dynamic interactions among workers -- has remained unaddressed. This paper offers a theoretical analysis explaining why, how, and when these intermediate, hierarchical updates lead to practical and provable convergence in distributed environments. Despite being a theoretical work, our prototype implementation demonstrates that such a distributed PCA algorithm converges effectively and in scalable way: through experiments, our proposed framework offers comparable performance to EigenGame-$\mu$, the state-of-the-art model-parallel PCA solver.