In this paper, we address the challenging problem of selecting tuningparameters for high-dimensional sparse regression. We propose a simple andcomputationally efficient method, called path thresholding (PaTh), thattransforms any tuning parameter-dependent sparse regression algorithm into anasymptotically tuning-free sparse regression algorithm. More specifically, weprove that, as the problem size becomes large (in the number of variables andin the number of observations), PaTh performs accurate sparse regression, underappropriate conditions, without specifying a tuning parameter. Infinite-dimensional settings, we demonstrate that PaTh can alleviate thecomputational burden of model selection algorithms by significantly reducingthe search space of tuning parameters.
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