| Summary: | We consider the tradeoffs between statistical accuracy and computational complexity in 3 concrete settings. In the first, we use hard-thresholding of the sample covariance together with l2-regularization to derive a family of estimators that provide a tuneable tradeoff between statistical risk and computational efficiency in the linear regression setting. In the second example, we consider inference and hypothesis testing for l 1-penalized linear regression. We again use hard-thresholding of the sample covariance matrix to get a computational speed-up, but this time we show that asymptotically there is no loss of power. Finally, we consider kernel regression and the nonparametric setting. We use variants of locality-sensitive hashing to more efficiently compute the classical kernel smoothing estimator. The bandwidth together with the parameters of the hashing algorithm control the tradeoff between the computational complexity and predictive risk of the procedure.
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