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Cross-validation (CV) is a popular approach for assessing and selecting predictive models. However, when the number of folds is large, CV suffers from a need to repeatedly refit a learning procedure on a large number of training datasets.…
We investigate leave-one-out cross validation (CV) as a determinator of the weight of the penalty term in the least absolute shrinkage and selection operator (LASSO). First, on the basis of the message passing algorithm and a perturbative…
Cross-validation (CV) methods are popular for selecting the tuning parameter in the high-dimensional variable selection problem. We show the mis-alignment of the CV is one possible reason of its over-selection behavior. To fix this issue,…
Recently, new methods for model assessment, based on subsampling and posterior approximations, have been proposed for scaling leave-one-out cross-validation (LOO) to large datasets. Although these methods work well for estimating predictive…
Statistical machine learning models should be evaluated and validated before putting to work. Conventional k-fold Monte Carlo Cross-Validation (MCCV) procedure uses a pseudo-random sequence to partition instances into k subsets, which…
Two key tasks in high-dimensional regularized regression are tuning the regularization strength for accurate predictions and estimating the out-of-sample risk. It is known that the standard approach -- $k$-fold cross-validation -- is…
Cross-validation (CV) is one of the main tools for performance estimation and parameter tuning in machine learning. The general recipe for computing CV estimate is to run a learning algorithm separately for each CV fold, a computationally…
Cross-validation can be used to measure a model's predictive accuracy for the purpose of model comparison, averaging, or selection. Standard leave-one-out cross-validation (LOO-CV) requires that the observation model can be factorized into…
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…
The asymptotic optimality (a.o.) of various hyper-parameter estimators with different optimality criteria has been studied in the literature for regularized least squares regression problems. The estimators include e.g., the maximum…
The lasso procedure is ubiquitous in the statistical and signal processing literature, and as such, is the target of substantial theoretical and applied research. While much of this research focuses on the desirable properties that lasso…
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…
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,…
K-fold cross validation (CV) is a popular method for estimating the true performance of machine learning models, allowing model selection and parameter tuning. However, the very process of CV requires random partitioning of the data and so…
Bayesian cross-validation (CV) is a popular method for predictive model assessment that is simple to implement and broadly applicable. A wide range of CV schemes is available for time series applications, including generic leave-one-out…
It is useful to estimate the expected predictive performance of models planned to be used for prediction. We focus on leave-one-out cross-validation (LOO-CV), which has become a popular method for estimating predictive performance of…
It is crucial to assess the predictive performance of a model to establish its practicality and relevance in real-world scenarios, particularly for high-dimensional data analysis. Among data splitting or resampling methods, cross-validation…
Recent years have seen substantial advances in our understanding of high-dimensional ridge regression, but existing theories assume that training examples are independent. By leveraging techniques from random matrix theory and free…
In a wide variety of sequential decision making problems, it can be important to estimate the impact of rare events in order to minimize risk exposure. A popular risk measure is the conditional value-at-risk (CVaR), which is commonly…
K-fold cross-validation (CV) with squared error loss is widely used for evaluating predictive models, especially when strong distributional assumptions cannot be taken. However, CV with squared error loss is not free from distributional…