Least Squares Regression Can Exhibit Under-Parameterized Double Descent
Keywords: Learning Theory, Generalization, Random Matrix Theory, High Dimensional Statistics
TL;DR: We show that the current theory for double descent is incomplete
Abstract: The relationship between the number of training data points, the number of parameters, and the generalization capabilities of models has been widely studied. Previous work has shown that double descent can occur in the over-parameterized regime and that the standard bias-variance trade-off holds in the under-parameterized regime. These works provide multiple reasons for the existence of the peak. We postulate that the location of the peak depends on the technical properties of both the spectrum as well as the eigenvectors of the sample covariance. We present two simple examples that provably exhibit double descent in the under-parameterized regime and do not seem to occur for reasons provided in prior work.
Primary Area: Learning theory
Submission Number: 3453
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