More Data Can Hurt for Linear Regression: Sample-wise Double Descent
This is an incremental theoretical insight into double-descent phenomena, relevant for researchers in machine learning theory.
The paper demonstrates that in overparameterized linear regression, adding more samples can increase test risk due to a bias-variance tradeoff where bias decreases but variance rises, with this phenomenon observed in simple isotropic Gaussian settings.
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.