  Feature screening is a powerful tool in the analysis of high dimensional
data. When the sample size $N$ and the number of features $p$ are both large,
the implementation of classic screening methods can be numerically challenging.
In this paper, we propose a distributed screening framework for big data setup.
In the spirit of "divide-and-conquer", the proposed framework expresses a
correlation measure as a function of several component parameters, each of
which can be distributively estimated using a natural U-statistic from data
segments. With the component estimates aggregated, we obtain a final
correlation estimate that can be readily used for screening features. This
framework enables distributed storage and parallel computing and thus is
computationally attractive. Due to the unbiased distributive estimation of the
component parameters, the final aggregated estimate achieves a high accuracy
that is insensitive to the number of data segments $m$ specified by the problem
itself or to be chosen by users. Under mild conditions, we show that the
aggregated correlation estimator is as efficient as the classic centralized
estimator in terms of the probability convergence bound; the corresponding
screening procedure enjoys sure screening property for a wide range of
correlation measures. The promising performances of the new method are
supported by extensive numerical examples.
