Provable Model-Parallel Distributed Principal Component Analysis with Parallel Deflation

2025-02-24

AI Summary

Existing distributed PCA methods lack theoretical convergence guarantees when workers asynchronously optimize distinct principal components. Method: We propose the first model-parallel framework for distributed PCA with provable linear convergence. Instead of relying on deflation—a sequential, dependency-prone approach—we introduce a centralized, dynamic hierarchical information exchange mechanism that enables asynchronous updates and incurs low communication overhead. Contribution/Results: Our key theoretical contribution is the first rigorous convergence analysis framework for distributed, dynamic inter-worker interaction, integrating tools from distributed optimization, random matrix theory, and asynchronous iteration analysis. Experiments demonstrate that our prototype system matches the convergence speed and scalability of the state-of-the-art solver EigenGame-μ, thereby bridging a critical gap between theoretical convergence guarantees and efficient practical implementation in distributed PCA.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

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.

Problem

• Distributed PCA with parallel deflation
• Asynchronous updates in distributed environments
• Theoretical convergence of hierarchical worker interactions

Innovation

• Distributed PCA framework
• Asynchronous worker updates
• Provable convergence analysis