More Data Can Hurt for Linear Regression: Sample-wise Double Descent
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Publication:6331173
arXiv1912.07242MaRDI QIDQ6331173
Author name not available (Why is that?)
Publication date: 16 December 2019
Abstract: In this expository note we describe a surprising phenomenon in overparameterized linear regression, where the dimension exceeds the number of samples: there is a regime where the test risk of the estimator found by gradient descent increases with additional samples. In other words, more data actually hurts the estimator. This behavior is implicit in a recent line of theoretical works analyzing "double-descent" phenomenon in linear models. In this note, we isolate and understand this behavior in an extremely simple setting: linear regression with isotropic Gaussian covariates. In particular, this occurs due to an unconventional type of bias-variance tradeoff in the overparameterized regime: the bias decreases with more samples, but variance increases.
Has companion code repository: https://github.com/IyarLin/paper_results_reproduction
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