Regularization with Fake Features

Recent successes of massively overparameterized models have inspired a new line of work investigating the underlying conditions that enable overparameterized models to generalize well. This paper considers a framework where the possibly overparametrized model includes fake features, i.e., features that are present in the model but not in the data. We present a non-asymptotic high-probability bound on the generalization error of the ridge regression problem under the model misspecification of having fake features. Our high-probability results characterize the interplay between the implicit regularization provided by the fake features and the explicit regularization provided by the ridge parameter. We observe that fake features may improve the generalization error, even though they are irrelevant to the data.