Journal
JOURNAL OF MACHINE LEARNING RESEARCH
Volume 21, Issue -, Pages -Publisher
MICROTOME PUBL
Keywords
Distributed estimation; high-dimensional linear model; quantile loss; robust estimator; support recovery
Funding
- NSF [IIS-1845444]
- National Program on Key Basic Research Project (973 Program) [2018AAA0100704]
- NSFC [11825104, 11690013]
- Youth Talent Support Program
- Australian Research Council
- Shanghai Sailing Program [19YF1402800]
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This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss function instead of the commonly used squared loss. However, the non-smooth quantile loss poses new challenges to high-dimensional distributed estimation in both computation and theoretical development. To address the challenge, we transform the response variable and establish a new connection between quantile regression and ordinary linear regression. Then, we provide a distributed estimator that is both computationally and communicationally efficient, where only the gradient information is communicated at each iteration. Theoretically, we show that, after a constant number of iterations, the proposed estimator achieves a near-oracle convergence rate without any restriction on the number of machines. Moreover, we establish the theoretical guarantee for the support recovery. The simulation analysis is provided to demonstrate the effectiveness of our method.
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