Wang, Xiangyu, Dunson, David B. and Leng, Chenlei (2016) DECOrrelated feature space partitioning for distributed sparse regression. In: 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain, 5-10 Dec 2016. Published in: Advances in Neural Information Processing Systems (NIPS 2016), 29 ISSN 1049-5258. (In Press)

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Abstract

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space). While the majority of the literature focuses on sample space partitioning, feature space partitioning is more effective when p >> n. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In this paper, we solve these problems through a new embarrassingly parallel framework named DECO for distributed variable selection and parameter estimation. In DECO, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

Item Type:	Conference Item (Paper)
Divisions:	Faculty of Science > Statistics
Journal or Publication Title:	Advances in Neural Information Processing Systems (NIPS 2016)
Publisher:	Morgan Kaufmann Publishers, Inc.
ISSN:	1049-5258
Official Date:	16 November 2016
Dates:	Date Event 16 November 2016 Accepted
Volume:	29
Status:	Peer Reviewed
Publication Status:	In Press
Access rights to Published version:	Restricted or Subscription Access
Conference Paper Type:	Paper
Title of Event:	30th Conference on Neural Information Processing Systems (NIPS 2016)
Type of Event:	Conference
Location of Event:	Barcelona, Spain
Date(s) of Event:	5-10 Dec 2016
Related URLs:	Organisation

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