Near-optimal stochastic approximation for online principal component estimation
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Publication:681490
DOI10.1007/S10107-017-1182-ZzbMATH Open1414.62214arXiv1603.05305OpenAlexW2298720961MaRDI QIDQ681490
Author name not available (Why is that?)
Publication date: 12 February 2018
Published in: (Search for Journal in Brave)
Abstract: Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests. Despite its rich applications, theoretical convergence analysis remains largely open. In this paper, we cast online PCA into a stochastic nonconvex optimization problem, and we analyze the online PCA algorithm as a stochastic approximation iteration. The stochastic approximation iteration processes data points incrementally and maintains a running estimate of the principal component. We prove for the first time a nearly optimal finite-sample error bound for the online PCA algorithm. Under the subgaussian assumption, we show that the finite-sample error bound closely matches the minimax information lower bound.
Full work available at URL: https://arxiv.org/abs/1603.05305
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