Optimal Two-Step Prediction in Regression

2014/10/18 by Chételat, Didier, Lederer, Johannes, Salmon, Joseph
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1410.5014

Abstract

High-dimensional prediction typically comprises two steps: variable selection and subsequent least-squares refitting on the selected variables. However, the standard variable selection procedures, such as the lasso, hinge on tuning parameters that need to be calibrated. Cross-validation, the most popular calibration scheme, is computationally costly and lacks finite sample guarantees. In this paper, we introduce an alternative scheme, easy to implement and both computationally and theoretically efficient.

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