In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for empirical risk minimizers. In the general setting, we prove sanity-check bounds in the spirit of \cite{KR99} \textquotedblleft\textit{bounds showing that the worst-case error of this estimate is not m…
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48 results for “Generalized cross-validation”
In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for subagged estimators, both for classification and regressor. General loss functions and class of predictors with both finite and infinite VC-dimension are considered. We slightly generalize the formali…
In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for stable predictors in the context of risk assessment. The notion of stability has been first introduced by \cite{DEWA79} and extended by \cite{KEA95}, \cite{BE01} and \cite{KUNIY02} to characterize cla…
The paper develops a cross-validation method for improving signal denoising techniques.
problem Improving signal denoising methods for nonparametric regression.
method Develops a general cross-validation framework for signal denoising and applies it to Trend Filtering and Dyadic CART.
result Cross validated versions of Trend Filtering and Dyadic CART achieve nearly optimal convergence rates.
Cross-validation is the workhorse of modern applied statistics and machine learning, as it provides a principled framework for selecting the model that maximizes generalization performance. In this paper, we show that the cross-validation risk is differentiable with respect to the hyperparameters and training data for …
Nested cross-validation when selecting classifiers is overzealous for most practical applicationscs.LG
When selecting a classification algorithm to be applied to a particular problem, one has to simultaneously select the best algorithm for that dataset \emph{and} the best set of hyperparameters for the chosen model. The usual approach is to apply a nested cross-validation procedure; hyperparameter selection is performed…
In this paper, we introduce a new concept of stability for cross-validation, called the -stability, and use it as a new perspective to build the general theory for cross-validation. The -stability mathematically connects the generalization ability and the stability of…
Study evaluates cross-validation methods for clinical ECG classification, finding leave-source-out more reliable.
problem Overoptimistic cross-validation estimates for new patient sources.
method Empirical evaluation of K-fold and leave-source-out cross-validation methods.
result Leave-source-out cross-validation provides more reliable performance estimates.
We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we show that it is non-trivial to select a good estimator without knowledge about the …
New method for cross-validation in high-dimensional data with dependent or heavy-tailed covariates.
problem Inconsistent cross-validation in high-dimensional settings with dependent or heavy-tailed covariates.
method ROTI-GCV framework for cross-validation under proportional asymptotics regime.
result Demonstrated accuracy of ROTI-GCV in synthetic and semi-synthetic settings.
This paper improves model selection with cross-validation using domain knowledge.
problem Improving model selection with cross-validation risk estimation.
method Establishes distribution-free deviation bounds using VC dimension, formalizes Learning Spaces based on domain knowledge.
result Enhanced generalization through selection of candidate models based on domain knowledge.
Fast calculation of Gaussian Process multiple-fold cross-validation residuals and their covariancesstat.ME
We speed up Gaussian process cross-validation calculations and improve model diagnostics.
problem Efficiently calculating cross-validation residuals and their covariances in Gaussian processes.
method Generalized fast Gaussian process leave-one-out formulae to multiple-fold cross-validation, highlighting covariance structures.
result Correcting for residual covariances in cross-validation improves back to Maximum Likelihood Estimation.
While many statistical models and methods are now available for network analysis, resampling network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but is not directly applicable to networks since splitting network nodes into groups requires delet…
A fast bootstrap method estimates cross-validation standard error.
problem Uncertainty quantification in cross-validation estimates.
method Random-effects model to estimate variance component.
result Valid confidence intervals for model performance.
Analysis of cross-validation for early-stopped gradient descent in high-dimensional regression.
problem Inconsistency of GCV for early-stopped GD in high-dimensional least squares regression.
method Theoretical analysis of GCV and LOOCV applied to early-stopped GD in high-dimensional least squares regression.
result LOOCV converges uniformly to the prediction risk of early-stopped GD, while GCV is generically inconsistent.
New cross-validation methods for Gaussian process regression with efficient gradient computation.
problem Estimating parameters of Gaussian process covariance functions.
method Derive new cross-validation criteria and efficient adjoint computation of gradients.
result Efficient method for evaluating cross-validation criteria and their gradients.
Cross-validation estimates model performance on unseen data, not training data.
problem Understanding how cross-validation estimates prediction error and its limitations.
method Analyzing linear models and popular prediction error estimates, introducing nested cross-validation.
result Cross-validation estimates the average prediction error of models fit on other unseen training sets, not the model at hand.
Improves test set performance and reduces out-of-sample disappointment for unstable models.
problem Ensuring strong test set performance via cross-validation for unstable models.
method Nested k-fold cross-validation with hyperparameter selection based on a weighted sum of cross-validation metric and model stability measure.
result Improves out-of-sample MSE for sparse ridge regression and CART by 4% and 2% respectively, compared to k-fold cross-validation.
Optimizes Lasso hyperparameters using leave-one-out CV.
problem Finding optimal hyperparameters for Lasso regression.
method Develops an algorithm to compute exact or approximate leave-one-out CV.
result Algorithm finds optimal hyperparameters for Lasso.
A new method improves super learner validation efficiency.
problem Improving the efficiency of super learner validation.
method Bootstrap Bias Corrected Cross Validation applied to Super Learning.
result Bootstrap Bias Corrected Cross Validation proved efficient and cost-effective.
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 usually causes subsampling bias, inflates generalization errors and jeopardizes the r…
Cross-validation methods help learn dynamical systems from data.
problem Learning surrogate models for dynamical systems from limited data.
method Variants of cross-validation (Kernel Flows, MMD, Lyapunov exponents).
result Simple approaches for kernel selection in dynamical system emulators.
Cross-validationmath.ST
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 family. For the risk estimation problem, we compute the bias (which can also be …
The paper improves confidence intervals for test error using cross-validation.
problem Improving confidence intervals for test error in machine learning.
method Develops central limit theorems and consistent estimators for cross-validation.
result Provides asymptotically-exact confidence intervals and hypothesis tests.
Cross validation residuals are well known for the ordinary least squares model. Here leave-M-out cross validation is extended to generalised least squares. The relationship between cross validation residuals and Cook's distance is demonstrated, in terms of an approximation to the difference in the generalised residual …
CV inference can be invalid for relatively unstable model comparisons.
problem The validity of cross-validation for model comparison is questioned when models are relatively unstable.
method The study proves that simple, individually stable models can generate relatively unstable comparisons, invalidating CV inference.
result The Lasso and soft-thresholding generate relatively unstable comparisons, invalidating CV inferences.
A new cross-validation method reduces redundancy and improves model performance.
problem Redundancy in traditional k-fold cross-validation leads to biased results.
method Irredundant k-fold cross-validation, where each instance is used exactly once for training and testing.
result Consistent performance estimates with reduced variance and lower computational cost.
The paper shows cross-validation fails in learning Gaussian graphical model structures.
problem Cross-validation's failure in learning Gaussian graphical model structures.
method Finite-sample bounds on misidentification probability of Lasso estimator.
result Cross-validation is inconsistent for learning Gaussian graphical model structures.
With the increasing size of today's data sets, finding the right parameter configuration in model selection via cross-validation can be an extremely time-consuming task. In this paper we propose an improved cross-validation procedure which uses nonparametric testing coupled with sequential analysis to determine the bes…
Proposes a new cross-validation method to estimate model performance.
problem The standard cross-validation method does not accurately estimate the performance of the recommended model.
method Develops a new random-effects model framework to improve naive cross-validation estimators.
result Proposed estimators outperform conventional and naive methods in estimating model performance.
Study compares mutation validation and cross-validation for model selection.
problem Comparing model selection methods for generalization performance and computational efficiency.
method Empirical comparison using benchmark and real-world datasets with Bayesian tests.
result Both methods select models with equivalent generalization performance but MV selects simpler models and is computationally cheaper.
A new method controls risk for set predictors using cross-validation.
problem Inefficient set predictors when data limited.
method Cross-validation conformal risk control (CV-CRC).
result CV-CRC offers theoretical guarantees and reduces set size.
Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of cross-validation procedures. This survey intends to relate these results to the most recen…
We consider a priori generalization bounds developed in terms of cross-validation estimates and the stability of learners. In particular, we first derive an exponential Efron-Stein type tail inequality for the concentration of a general function of n independent random variables. Next, under some reasonable notion of s…
ECV method optimizes ensemble parameters for randomized ensembles.
problem Efficient tuning of ensemble parameters in randomized ensembles.
method ECV (Extrapolated Cross-Validation) method for tuning ensemble and subsample sizes.
result ECV yields δ-optimal ensembles for squared prediction risk.
Cross-validation is one of the most popular model selection methods in statistics and machine learning. Despite its wide applicability, traditional cross validation methods tend to select overfitting models, due to the ignorance of the uncertainty in the testing sample. We develop a new, statistically principled infere…
K-fold Cross Validation is commonly used to evaluate classifiers and tune their hyperparameters. However, it assumes that data points are Independent and Identically Distributed (i.i.d.) so that samples used in the training and test sets can be selected randomly and uniformly. In Human Activity Recognition datasets, we…
The paper assesses quality measures for machine learning models using cross-validation.
problem Evaluating the accuracy and robustness of quality measures for machine learning models.
method Cross-validation approach to estimate prediction error and quantify explained variation. Confidence bounds and local quality measures derived from residuals.
result The reliability and robustness of quality measures are assessed through numerical examples and confidence bounds.
New CV method reduces bias in spatial prediction models.
problem Bias in standard cross-validation due to uneven sampling.
method Target-Weighted Cross-Validation (TWCV) framework.
result Weighted CV approaches reduce bias in prediction error.
Optimal data splitting improves covariance matrix estimation in large datasets.
problem Improving large covariance matrix estimation in high-dimensional settings.
method Focus on holdout method, derive closed-form error expression, connect to eigenvalue variance.
result Optimal train-test split scales as square root of matrix dimension.
Tuning parameter selection is of critical importance for kernel ridge regression. To this date, data driven tuning method for divide-and-conquer kernel ridge regression (d-KRR) has been lacking in the literature, which limits the applicability of d-KRR for large data sets. In this paper, by modifying the Generalized Cr…
The paper proves LOO CV is reliable under estimator stability.
problem Ensuring the reliability of leave-one-out cross validation.
method Using concentration inequalities based on logarithmic Sobolev inequality.
result LOO CV is a valid procedure under estimator stability.
The lasso and related sparsity inducing algorithms have been the target of substantial theoretical and applied research. Correspondingly, many results are known about their behavior for a fixed or optimally chosen tuning parameter specified up to unknown constants. In practice, however, this oracle tuning parameter is …
LOOCV is often useful for analyzing small, structured experimental designs.
problem The effectiveness of cross-validation in analyzing designed experiments.
method Empirical study comparing LOOCV and other model selection methods.
result LOOCV is often useful in the analysis of small, structured experimental designs.
Improved LOO cross-validation for function approximation.
problem Estimating the Integrated Squared Error (ISE) for function approximation.
method Weighted Leave-One-Out cross-validation based on Gaussian Process.
result Significantly more precise ISE estimation compared to unweighted LOO.
A method for efficient CV estimates in Bayesian hierarchical models.
problem Computational infeasibility of cross-validation in Bayesian hierarchical regression models.
method Conditioning on variance-covariance parameters to transform CV into an optimization problem.
result Equivalent or improved predictive estimates compared to full cross-validation.
We show how to adjust the coefficient of determination () when used for measuring predictive accuracy via leave-one-out cross-validation.
The Theory Behind Overfitting, Cross Validation, Regularization, Bagging, and Boosting: Tutorialstat.ML
In this tutorial paper, we first define mean squared error, variance, covariance, and bias of both random variables and classification/predictor models. Then, we formulate the true and generalization errors of the model for both training and validation/test instances where we make use of the Stein's Unbiased Risk Estim…