Communication-efficient Algorithms for Distributed Stochastic Principal Component Analysis

Abstract

We study the fundamental problem of Principal Component Analysis in a statistical distributed setting in which each machine out of $m$ stores a sample of $n$ points sampled i.i.d. from a single unknown distribution. We study algorithms for estimating the leading principal component of the population covariance matrix that are both communication-efficient and achieve estimation error of the order of the centralized ERM solution that uses all $mn$ samples. On the negative side, we show that in contrast to results obtained for distributed estimation under convexity assumptions, for the PCA objective, simply averaging the local ERM solutions cannot guarantee error that is consistent with the centralized ERM. We show that this unfortunate phenomena can be remedied by performing a simple correction step which correlates between the individual solutions, and provides an estimator that is consistent with the centralized ERM for sufficiently-large $n$. We also introduce an iterative distributed algorithm that is applicable in any regime of $n$, which is based on distributed matrix-vector products. The algorithm gives significant acceleration in terms of communication rounds over previous distributed algorithms, in a wide regime of parameters.

References in corpus (5)

• Communication Efficient Distributed Optimization using an Approximate Newton-type Method
• AIDE: Fast and Communication Efficient Distributed Optimization
• Improved Distributed Principal Component Analysis
• Fast and Simple PCA via Convex Optimization
• Streaming PCA: Matching Matrix Bernstein and Near-Optimal Finite Sample Guarantees for Oja's Algorithm

Cited by in corpus (8)

• Distributed Estimation of Principal Eigenspaces
• Distributed Stochastic Algorithms for High-rate Streaming Principal Component Analysis
• On the Gap Between Strict-Saddles and True Convexity: An Omega(log d) Lower Bound for Eigenvector Approximation
• Communication-Efficient Distributed SVD via Local Power Iterations
• Distributed Estimation for Principal Component Analysis: an Enlarged Eigenspace Analysis
• Analog MIMO Communication for One-shot Distributed Principal Component Analysis
• One-shot Distibuted Algorithm for PCA with RBF Kernels
• FedPower: Privacy-Preserving Distributed Eigenspace Estimation