Provable Model-Parallel Distributed Principal Component Analysis with Parallel Deflation

TL;DR

This paper introduces a provable, asynchronous distributed PCA algorithm inspired by deflation methods, enabling scalable, efficient eigenvector computation with theoretical guarantees and competitive empirical performance.

Contribution

It provides the first theoretical analysis of distributed, dynamic interactions in PCA with asynchronous updates, breaking the sequential deflation dependency.

Findings

The algorithm converges effectively in distributed settings.

It achieves performance comparable to state-of-the-art methods.

Theoretical analysis explains convergence conditions and mechanisms.

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.