Optimal Sub-sampling with Influence Functions
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Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the concept of an asymptotically linear estimator and the associated influence function leads to optimal sampling procedures for a wide class of popular models. Furthermore, for linear regression models which have well-studied procedures for non-uniform sub-sampling, we show our optimal influence function based method outperforms previous approaches. We empirically show the improved performance of our method on real datasets.
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