Subset Selection with Shrinkage: Sparse Linear Modeling when the SNR is low

We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best-subsets selection, which minimizes the residual sum of squares subject to a constraint on the number of nonzero coefficients. While the best-subsets selection procedure is often perceived as the "gold standard" in sparse learning when the signal to noise ratio (SNR) is high, its predictive performance deteriorates when the SNR is low... (read more)

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