Two models of double descent for weak features. Belkin, M., Hsu, D., & Xu, J. , 2019. abstract bibtex The "double descent" risk curve was recently proposed to qualitatively describe the out-of-sample prediction accuracy of variably-parameterized machine learning models. This article provides a precise mathematical analysis for the shape of this curve in two simple data models with the least squares/least norm predictor. Specifically, it is shown that the risk peaks when the number of features \$p\$ is close to the sample size \$n\$, but also that the risk decreases towards its minimum as \$p\$ increases beyond \$n\$. This behavior is contrasted with that of "prescient" models that select features in an a priori optimal order.
@Article{Belkin2019,
author = {Belkin, Mikhail and Hsu, Daniel and Xu, Ji},
title = {Two models of double descent for weak features},
journal = {},
volume = {},
number = {},
pages = {},
year = {2019},
abstract = {The \"double descent\" risk curve was recently proposed to qualitatively describe the out-of-sample prediction accuracy of variably-parameterized machine learning models. This article provides a precise mathematical analysis for the shape of this curve in two simple data models with the least squares/least norm predictor. Specifically, it is shown that the risk peaks when the number of features \$p\$ is close to the sample size \$n\$, but also that the risk decreases towards its minimum as \$p\$ increases beyond \$n\$. This behavior is contrasted with that of \"prescient\" models that select features in an a priori optimal order.},
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keywords = {}}
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