Related papers: Estimation Stability with Cross Validation (ESCV)
The application of immersed boundary methods in static analyses is often impeded by poorly cut elements (small cut elements problem), leading to ill-conditioned linear systems of equations and stability problems. While these concerns may…
Despite ongoing theoretical research on cross-validation (CV), many theoretical questions remain widely open. This motivates our investigation into how properties of algorithm-distribution pairs can affect the choice for the number of folds…
Machine learning models experience deteriorated performance when trained in the presence of noisy labels. This is particularly problematic for medical tasks, such as survival prediction, which typically face high label noise complexity with…
Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the…
Model selection is difficult to analyse yet theoretically and empirically important, especially for high-dimensional data analysis. Recently the least absolute shrinkage and selection operator (Lasso) has been applied in the statistical and…
In spite of the wealth of literature on the theoretical properties of the Lasso, there is very little known when the value of the tuning parameter is chosen using the data, even though this is what actually happens in practice. We give a…
Nonparametric varying coefficient (NVC) models are useful for modeling time-varying effects on responses that are measured repeatedly for the same subjects. When the number of covariates is moderate or large, it is desirable to perform…
The adaptive lasso refers to a class of methods that use weighted versions of the $L_1$-norm penalty, with weights derived from an initial estimate of the parameter vector to be estimated. Irrespective of the method chosen to compute this…
We introduce a novel cross-validation method that we call latinCV and we compare this method to other model selection methods using data generated from a stochastic block model. Comparing latinCV to other cross-validation methods, we show…
Model comparison is the cornerstone of theoretical progress in psychological research. Common practice overwhelmingly relies on tools that evaluate competing models by balancing in-sample descriptive adequacy against model flexibility, with…
Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or…
Crystallization is one of the most important physicochemical processes which has relevance in material science, biology, and the environment. Decades of experimental and theoretical efforts have been made to understand this fundamental…
We revisit the problem of ensuring strong test set performance via cross-validation, and propose a nested k-fold cross-validation scheme that selects hyperparameters by minimizing a weighted sum of the usual cross-validation metric and an…
The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…
We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…
Cross-validation (CV) is a widely-used method of predictive assessment based on repeated model fits to different subsets of the available data. CV is applicable in a wide range of statistical settings. However, in cases where data are not…
In this paper, we derive non-asymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using $K$-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly…
Consider the following class of learning schemes: $$\hat{\boldsymbol{\beta}} := \arg\min_{\boldsymbol{\beta}}\;\sum_{j=1}^n \ell(\boldsymbol{x}_j^\top\boldsymbol{\beta}; y_j) + \lambda R(\boldsymbol{\beta}),\qquad\qquad (1) $$ where…
Cross-validation (CV) is a technique used to estimate generalization error for prediction models. For pipeline modeling algorithms (i.e. modeling procedures with multiple steps), it has been recommended the entire sequence of steps be…
In this paper, for Lasso penalized linear regression models in high-dimensional settings, we propose a modified cross-validation method for selecting the penalty parameter. The methodology is extended to other penalties, such as Elastic…