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arXiv · 1903.07571

Two models of double descent for weak features

Mikhail Belkin·Daniel Hsu·Ji Xu
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Abstract

The "double descent" risk curve was 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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Mikhail Belkin, Daniel Hsu, Ji Xu. 2019-03-18. Two models of double descent for weak features. https://doi.org/10.1137/20m1336072

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