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Subsampling is a popular approach to alleviating the computational burden foranalyzing massive datasets. Recent efforts have been devoted to variousstatistical models without explicit regularization. In this paper, we developan efficient subsampling procedure for the large sample linear ridgeregression. In contrast to the ordinary least square estimator, theintroduction of the ridge penalty leads to a subtle trade-off between bias andvariance. We first investigate the asymptotic properties of the subsamplingestimator and then propose to minimize the asymptotic-mean-squared-errorcriterion for optimality. The resulting subsampling probability involves bothridge leverage score and L2 norm of the predictor. To further reduce thecomputational cost for calculating the ridge leverage scores, we propose thealgorithm with efficient approximation. We show by synthetic and real datasetsthat the algorithm is both statistically accurate and computationally efficientcompared with existing subsampling based methods.

Optimal Subsampling for Large Sample Ridge Regression