10 accepted papers
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 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…
Standard conformal prediction methods provide a marginal coverage guarantee, which means that for a random test point, the conformal prediction set contains the true label with a user-specified probability. In many classification problems, we would like to obtain a stronger guarantee--that for test…
We study the problem of uncertainty quantification for time series prediction, with the goal of providing easy-to-use algorithms with formal guarantees. The algorithms we present build upon ideas from conformal prediction and control theory, are able to prospectively model conformal scores in an on…
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…
In this paper we study the statistical properties of Laplacian smoothing, a graph-based approach to nonparametric regression. Under standard regularity conditions, we establish upper bounds on the error of the Laplacian smoothing estimator \smash{$\widehat{f}$}, and a goodness-of-fit test also based…
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…
We study the implicit regularization of mini-batch stochastic gradient descent, when applied to the fundamental problem of least squares regression. We leverage a continuous-time stochastic differential equation having the same moments as stochastic gradient descent, which we call stochastic gradien…
Given a statistical estimation problem where regularization is performed according to the structure of a large, dense graph G, we consider fitting the statistical estimate using a \it sparsified surrogate graph \mathbfG, which shares the vertices of G but has far fewer edges, and is thus more tracta…
We introduce a family of adaptive estimators on graphs, based on penalizing the \ell_1 norm of discrete graph differences. This generalizes the idea of trend filtering (Kim et al., 2009, Tibshirani, 2014) used for univariate nonparametric regression, to graphs. Analogous to the univariate case, grap…