DECOrrelated feature space partitioning for distributed sparse regression
This addresses the problem of scalable sparse regression for high-dimensional data (p >> n) by providing an efficient distributed method that overcomes issues with correlations and dimension reduction, though it is incremental in improving existing partitioning approaches.
The paper tackles the computational challenge of fitting statistical models with large sample size or dimension by introducing DECO, a distributed framework for feature space partitioning that achieves consistent variable selection and parameter estimation with nearly minimax optimal convergence rates, independent of the number of partitions.
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 $p\gg n$. 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.