  Subsampling is a popular approach to alleviating the computational burden for
analyzing massive datasets. Recent efforts have been devoted to various
statistical models without explicit regularization. In this paper, we develop
an efficient subsampling procedure for the large sample linear ridge
regression. In contrast to the ordinary least square estimator, the
introduction of the ridge penalty leads to a subtle trade-off between bias and
variance. We first investigate the asymptotic properties of the subsampling
estimator and then propose to minimize the asymptotic-mean-squared-error
criterion for optimality. The resulting subsampling probability involves both
ridge leverage score and L2 norm of the predictor. To further reduce the
computational cost for calculating the ridge leverage scores, we propose the
algorithm with efficient approximation. We show by synthetic and real datasets
that the algorithm is both statistically accurate and computationally efficient
compared with existing subsampling based methods.
