Related papers: Optimal cross-validation in density estimation wit…

Cross-validation (CV) is widely used for tuning a model with respect to user-selected parameters and for selecting a "best" model. For example, the method of $k$-nearest neighbors requires the user to choose $k$, the number of neighbors,…

In this article, we rigorously establish the consistency of generalized cross-validation as a parameter-choice rule for solving inverse problems. We prove that the index chosen by leave-one-out GCV achieves a non-asymptotic, order-optimal…

We present a novel method for tuning the regularization hyper-parameter, $\lambda$, of a ridge regression that is faster to compute than leave-one-out cross-validation (LOOCV) while yielding estimates of the regression parameters of equal,…

Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression…

Conditional independence testing is an important problem, yet provably hard without assumptions. One of the assumptions that has become popular of late is called "model-X", where we assume we know the joint distribution of the covariates,…

Despite the tremendous empirical success of deep learning models to solve various learning tasks, our theoretical understanding of their generalization ability is very limited. Classical generalization bounds based on tools such as the VC…

We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…

Safe reinforcement learning (RL) focuses on training reward-maximizing agents subject to pre-defined safety constraints. Yet, learning versatile safe policies that can adapt to varying safety constraint requirements during deployment…

Vision-Language-Action (VLA) models excel in robotic manipulation but are constrained by their heavy reliance on expert demonstrations, leading to demonstration bias and limiting performance. Reinforcement learning (RL) is a vital…

In density estimation, the mean integrated squared error (MISE) is commonly used as a measure of performance. In that setting, the cross-validation criterion provides an unbiased estimator of the MISE minus the integral of the squared…

The One-versus-One (OvO) strategy is an approach of multi-classification models which focuses on training binary classifiers between each pair of classes. While the OvO strategy takes advantage of balanced training data, the classification…

Many versions of cross-validation (CV) exist in the literature; and each version though has different variants. All are used interchangeably by many practitioners; yet, without explanation to the connection or difference among them. This…

Studying unified model averaging estimation for situations with complicated data structures, we propose a novel model averaging method based on cross-validation (MACV). MACV unifies a large class of new and existing model averaging…

This text is a survey on cross-validation. We define all classical cross-validation procedures, and we study their properties for two different goals: estimating the risk of a given estimator, and selecting the best estimator among a given…

Evaluation metrics for prediction error, model selection and model averaging on space-time data are understudied and poorly understood. The absence of independent replication makes prediction ambiguous as a concept and renders evaluation…

We present a methodology for model evaluation and selection where the sampling mechanism violates the i.i.d. assumption. Our methodology involves a formulation of the bias between the standard Cross-Validation (CV) estimator and the mean…

In the world of targeted learning, cross-validated targeted maximum likelihood estimators, CV-TMLE [Zheng:2010aa], has a distinct advantage over TMLE [Laan:2006aa] in that one less condition is required of CV-TMLE in order to achieve…

A new method of bandwidth selection for kernel density estimators is proposed. The method, termed indirect cross-validation, or ICV, makes use of so-called selection kernels. Least squares cross-validation (LSCV) is used to select the…

Modern data analysis and statistical learning are marked by complex data structures and black-box algorithms. Data complexity stems from technologies such as imaging, remote sensing, wearable devices, and genomic sequencing. At the same…

We derive high-dimensional Gaussian comparison results for the standard $V$-fold cross-validated risk estimates. Our results combine a recent stability-based argument for the low-dimensional central limit theorem of cross-validation with…