  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.
