12 accepted papers
Self-distillation (SD), retraining a student on a mixture of ground-truth labels and a teacher’s own predictions using the same architecture and training data, often improves generalization empirically, but it is unclear when improvement is guaranteed. We study SD for ridge regression with an uncons…
We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent estimator for the risk. Specifically, we consider a heterogeneous collection of M?1 regularized M-estimators, each train…
"Model performance evaluation is a critical and expensive task in machine learning and computer vision. Without clear guidelines, practitioners often estimate model accuracy using a one-time completely random selection of the data. However, by employing tailored sampling and estimation strategies, o…
We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotica…
We analyze the statistical properties of generalized cross-validation (GCV) and leave-one-out cross-validation (LOOCV) applied to early-stopped gradient descent (GD) in high-dimensional least squares regression. We prove that GCV is generically inconsistent as an estimator of the prediction risk of…
We study the implicit regularization effects induced by (observation) weighting of pretrained features. For weight and feature matrices of bounded operator norms that are infinitesimally free with respect to (normalized) trace functionals, we derive equivalence paths connecting different weighting m…
We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train distribution. We establish general conditions that determine the sign of the optimal regularization level under covariate a…
How can we precisely estimate a large language model’s (LLM) accuracy on questions belonging to a specific topic within a larger question-answering dataset? The standard direct estimator, which averages the model’s accuracy on the questions in each subgroup, may exhibit high variance for subgroups (…
We establish precise structural and risk equivalences between subsampling and ridge regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic functionals of subsample ridge estimators, when fitted with different ridge regularization levels $\lambda$ and subsample…
We study subsampling-based ridge ensembles in the proportional asymptotics regime, where the feature size grows proportionally with the sample size such that their ratio converges to a constant. By analyzing the squared prediction risk of ridge ensembles as a function of the explicit penalty $\lambd…
We study the problem of estimating the distribution of the out-of-sample prediction error associated with ridge regression. In contrast, the traditional object of study is the uncentered second moment of this distribution (the mean squared prediction error), which can be estimated using cross-valida…
We examine generalized and leave-one-out cross-validation for ridge regression in a proportional asymptotic framework where the dimension of the feature space grows proportionally with the number of observations. Given i.i.d. samples from a linear model with an arbitrary feature covariance and a sig…