Related papers: ROTI-GCV: Generalized Cross-Validation for right-R…
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…
Covariate shift relaxes the widely-employed independent and identically distributed (IID) assumption by allowing different training and testing input distributions. Unfortunately, common methods for addressing covariate shift by trying to…
Robust estimators for linear regression require non-convex objective functions to shield against adverse affects of outliers. This non-convexity brings challenges, particularly when combined with penalization in high-dimensional settings.…
Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To…
Cross-validation (CV) is a popular method for model-selection. Unfortunately, it is not immediately obvious how to apply CV to unsupervised or exploratory contexts. This thesis discusses some extensions of cross-validation to unsupervised…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations,…
The concept of generalized cross-validation (GCV) is applied to modified total generalized variation (MTGV) regularization. Current implementations of the MTGV regularization rely on manual (or semi-manual) hyperparameter optimization,…
Randomized artificial neural networks such as extreme learning machines provide an attractive and efficient method for supervised learning under limited computing ressources and green machine learning. This especially applies when equipping…
In the present paper, we prove a new theorem, resulting in an update formula for linear regression model residuals calculating the exact k-fold cross-validation residuals for any choice of cross-validation strategy without model refitting.…
Learning models whose predictions are invariant under multiple environments is a promising approach for out-of-distribution generalization. Such models are trained to extract features $X_{\text{inv}}$ where the conditional distribution $Y…
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 conduct a non asymptotic study of the Cross Validation (CV) estimate of the generalization risk for learning algorithms dedicated to extreme regions of the covariates space. In this Extreme Value Analysis context, the risk function…
Leave-one-out cross-validation (LOOCV) can be particularly accurate among cross-validation (CV) variants for machine learning assessment tasks -- e.g., assessing methods' error or variability. But it is expensive to re-fit a model $N$ times…
As a technique that can compactly represent complex patterns, machine learning has significant potential for predictive inference. K-fold cross-validation (CV) is the most common approach to ascertaining the likelihood that a machine…
This paper investigates the efficiency of the K-fold cross-validation (CV) procedure and a debiased version thereof as a means of estimating the generalization risk of a learning algorithm. We work under the general assumption of uniform…
Generalized cross validation (GCV) is one of the most important approaches used to estimate parameters in the context of inverse problems and regularization techniques. A notable example is the determination of the smoothness parameter in…
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…
Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…
A fundamental problem in multivariate analysis is testing general linear hypotheses for regression coefficients in a multivariate linear model. This framework encompasses a wide range of well-studied tasks, including MANOVA, joint…