Fast and Robust Low-Rank Learning over Networks: A Decentralized Matrix Quantile Regression Approach

Decentralized low-rank learning is an active research domain with extensive practical applications. A common approach to producing low-rank and robust estimations is to employ a combination of the nonsmooth quantile regression loss and nuclear-norm regularizer. Nevertheless, directly applying existi...

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Bibliographic Details
Published in:Journal of computational and graphical statistics Vol. 33; no. 4; pp. 1214 - 1223
Main Authors: Qiao, Nan, Chen, Canyi
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 01.10.2024
Taylor & Francis Ltd
Subjects:
Algorithms
Convergence
Decentralized network
Efficiency
Heavy-tailed noise
Learning
Low-rank recovery
Quantile regression
Quantiles
Regression
Robustness
Scalable algorithms
Statistical analysis
ISSN:1061-8600, 1537-2715
Online Access:Get full text
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Summary:Decentralized low-rank learning is an active research domain with extensive practical applications. A common approach to producing low-rank and robust estimations is to employ a combination of the nonsmooth quantile regression loss and nuclear-norm regularizer. Nevertheless, directly applying existing techniques may result in slow convergence rates due to the doubly nonsmooth objective. To expedite the computation process, a decentralized surrogate matrix quantile regression method is proposed in this article. The proposed algorithm has a simple implementation and can provably converge at a linear rate. Additionally, we provide a statistical guarantee that our estimate can achieve an almost optimal convergence rate, regardless of the number of nodes. Numerical simulations confirm the efficacy of our approach.
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ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2024.2353640