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.
Active learning method improves local model validity estimation.
problem Ensuring local model validity in machine learning applications.
method Learning model error to estimate local validity using active learning.
result The proposed method can estimate local validity with a small amount of data.
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.
In this paper, we introduce a new concept of stability for cross-validation, called the (β,ϖ)-stability, and use it as a new perspective to build the general theory for cross-validation. The (β,ϖ)-stability mathematically connects the generalization ability and the stability of…
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.
Predictive models ground many state-of-the-art developments in statistical brain image analysis: decoding, MVPA, searchlight, or extraction of biomarkers. The principled approach to establish their validity and usefulness is cross-validation, testing prediction on unseen data. Here, I would like to raise awareness on e…
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.
The paper analyzes cross-validation for correlated data and introduces a bias-corrected estimator.
problem Cross-validation with squared error loss assumes independent and identically distributed (i.i.d.) data, which is often violated in correlated data.
method The paper presents a criterion for standard CV suitability and introduces a bias-corrected estimator (CVc) for correlated data. result The bias-corrected estimator (CVc) yields an unbiased estimate of prediction error in settings where standard CV is invalid. DD algorithm tracks test error from train error without validation data.
problem Systematic generalization gap between train and test errors in modern model training.
method Decoupled descent (DD) algorithm that cancels data reuse biases via approximate message passing.
result DD algorithm rigorously demonstrates zero-cost validation and 100% data utilization.
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…
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.
This work improves confidence intervals for Cox model test error using nested CV.
problem Insufficient understanding of confidence intervals for cross-validation in Cox model.
method Generalized nested cross-validation to Cox proportional hazards model.
result Improved coverage of confidence intervals for Cox model test error.
Machine learning improves official statistics but needs rigorous validation.
problem Lack of methodological robustness in machine learning for official statistics.
method Total Machine Learning Error (TMLE) framework to validate ML models.
result TMLE addresses representativeness and measurement errors in ML models.
A fast method for LOOCV in k-NN regression reduces computation time.
problem Efficient computation of LOOCV for k-NN regression.
method Identical LOOCV estimate to (k+1)-NN MSE on training data.
result LOOCV computation can be done with (k+1)-NN regression once.
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.
The paper introduces validated variational inference with practical error bounds.
problem Lack of accurate post-hoc measures for variational inference.
method The paper provides rigorous bounds on variational inference error.
result The bounds are widely applicable and computationally efficient.
Many decisions in healthcare, business, and other policy domains are made without the support of rigorous evidence due to the cost and complexity of performing randomized experiments. Using observational data to answer causal questions is risky: subjects who receive different treatments also differ in other ways that a…
Cross-validation pitfalls in change-point regression are addressed with new approaches.
problem Cross-validation's prediction error-based criterion may lead to under- or over-estimation of change-points.
method Proposes two approaches: absolute error loss and modified holdout sets.
result Consistent estimation of the number of change-points under certain conditions.
Robust variable selection for high-dimensional data with missing and measurement errors.
problem Missing data and measurement errors confound data distribution.
method Exponential loss function with inverse probability weighting and additive error models.
result The Atan punishment method improves robust variable selection.
Tutorial defines and explains overfitting, cross validation, regularization, bagging, and boosting.
problem Understanding and preventing overfitting in machine learning models.
method Defining and explaining mean squared error, variance, covariance, and bias; using Stein's Unbiased Risk Estimator (SURE); introducing cross validation, regularization, bagging, and boosting.
result Boosting prevents overfitting by reducing variance and improving generalization.
A method for making predictions with a reject option using conformal prediction.
problem Uncertainty in machine learning predictions, especially when models are unsure.
method Formalizing ML with reject option, using conformal prediction for distribution-free error guarantees.
result Theoretical guarantees on error rate for prediction sets with distribution-free validity.
New cross-validation method reduces bias and improves prediction error.
problem Subsampling bias in k-fold cross-validation.
method Best-discrepancy systematic sampling.
result Reduces subsampling bias and improves prediction error.
Study validates ML-UQ calibration statistics using simulated reference values.
problem Validation of ML-UQ calibration statistics is lacking due to lack of predefined reference values.
method Proposed validation workflow using simulated reference values derived from synthetic datasets.
result Some statistics, like CC and ENCE, are overly sensitive to generative distribution choice.
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.
Paper analyzes holdout cross-validation for large non-Gaussian covariance estimation.
problem Estimating large covariance matrices for non-Gaussian data.
method Use of Weingarten calculus and Ledoit-Péché formula for theoretical error derivation.
result Optimal train-test split ratio is proportional to square root of matrix dimension.
Method estimates uncertainty in spatial predictions by defining an 'area of applicability'.
problem Uncertainty in predictions for new geographic locations far from training data.
method Proposes a dissimilarity index (DI) based on minimum distance to training data, and defines the 'area of applicability' (AOA) using a threshold on DI.
result Prediction error within the AOA is comparable to the cross-validation error of the model, while cross-validation error does not apply outside the AOA.
Study reveals pervasive label errors in test sets, affecting machine learning benchmarks.
problem Label errors in test sets destabilize machine learning benchmarks.
method Identified label errors in 10 common datasets using confident learning algorithms and human validation.
result Lower capacity models may be more useful in real-world datasets with high proportions of erroneously labeled data.
The paper identifies overfitting as the main bottleneck in efficient deep reinforcement learning.
problem Improving sample efficiency in deep reinforcement learning.
method Empirical analysis on DMC tasks to identify overfitting as the main issue and developing a hill-climbing method targeting validation TD error.
result Overfitting is the primary bottleneck in sample-efficient deep RL, and regularization techniques can control this.
Normalizing Flows improve prediction interval efficiency in CP.
problem Inefficient prediction intervals in CP due to non-uniform error distribution.
method Train a Normalizing Flow to optimize the distance metric between errors and inputs.
result Optimized prediction intervals are more efficient and valid.
Framework for reliable prediction errors using Test-Time Dropout and Conformal Prediction.
problem Lack of reliable error computation for deep neural networks in drug discovery.
method Training a single neural network with dropout, applying it multiple times to validation and test sets, generating ensemble predictions, and using Conformal Prediction to compute errors.
result Dropout Conformal Predictors are valid and efficient, with narrower confidence intervals than RF-based Conformal Predictors.
ALO-CV approximates leave-one-out error in proportional regime.
problem Estimating generalization error in high-dimensional settings.
method Developed new analysis for ALO-CV, showed consistency under strong convexity.
result ALO-CV approximates leave-one-out error up to negligible error.
The paper improves ALO for ℓ1-regularized models.
problem Estimating out-of-sample error for ℓ1-regularized models. method Developed a novel theory for ℓ1-regularized problems, bounding ALO error. result For ℓ1-regularized problems, ALO error goes to zero as p goes to infinity. Study examines the cost of tuning hyper-parameters in regression models.
problem Estimating optimal hyper-parameters for regression models.
method Established finite-sample oracle inequalities for hyper-parameter selection.
result Generalization error of selected models shrinks at nearly a parametric rate.
The paper investigates overfitting in hyperparameter optimization.
problem Overfitting in hyperparameter optimization (overtuning).
method Formal definition, large-scale reanalysis of HPO benchmark data, analysis of factors affecting overtuning.
result Overtuning is more common than previously assumed, leading to worse generalization error in 10% of cases.
The paper analyzes trace regression with low-rank matrices under various regularization methods.
problem Estimating low-rank matrices with near-optimal error bounds under unknown regularization parameters.
method General spikiness notion, restricted strong convexity of sampling operator, cross-validation for parameter selection.
result Cross-validated estimators select near-optimal penalty parameters and outperform theory-inspired approaches.
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.
The paper extends conformal risk control to be valid with high probability over a growing calibration dataset.
problem Valid risk control over a growing calibration dataset.
method Quantile-based arguments for anytime-valid control.
result Guarantees remain valid with high probability over a cumulatively growing calibration dataset.
Analyzes error sources in global feature effect estimation methods.
problem Unexplored error sources in global feature effect estimation methods.
method Systematic, estimator-level analysis of bias and variance.
result Holdout data is theoretically cleanest, but estimation variance depends on sample size and model characteristics.
Transforms any test into anytime-valid with sample savings.
problem Sequential data invalidates classical test guarantees.
method Predicts test outcomes to create anytime-valid stopping rules.
result Ensures Type-I error control and near-optimal power.
The paper analyzes LOCV for high-dimensional risk estimation, proving error bounds.
problem Estimating out-of-sample prediction error in high-dimensional settings.
method Theoretical analysis of leave-one-out cross validation (LOCV) in penalized regression.
result Finite sample upper bounds on LOCV error, showing it converges to zero as n,p → ∞.
Study improves predictive performance testing for high-dimensional data using exhaustive nested cross-validation.
problem Reproducibility issues in K-fold cross-validation for high-dimensional data. method Proposes a novel predictive performance test based on exhaustive nested cross-validation, addressing computational complexity with a closed-form expression.
result Demonstrates the effectiveness of Ridge-based methods in high-dimensional predictive performance testing.
In this paper, we study the performance of extremum estimators from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. By adapting the classical concentration inequalities, we derive upper bounds on the empirical out-of-sample prediction e…
New method improves false-/true-positive-rate estimation in fraud detection with noisy labels.
problem Estimating FPR/TPR in fraud detection with class-conditional label noise.
method Directly cleaning model's validation data to de-correlate cleaning error with model scores.
result Improves accuracy of FPR/TPR estimates, especially in asymmetric label noise scenarios.
Careful tuning of a regularization parameter is indispensable in many machine learning tasks because it has a significant impact on generalization performances. Nevertheless, current practice of regularization parameter tuning is more of an art than a science, e.g., it is hard to tell how many grid-points would be need…
New method improves cross-validation for sparse reduced rank regression models.
problem Inconsistent parameter selection in cross-validation for high-dimensional data.
method Proposes cross-validation of projection-selection patterns to avoid inconsistency issues.
result Develops new scale-free information criteria for minimax optimal error rate.
A new method for fast, accurate cross-validation in high dimensions.
problem Efficiently approximating cross-validation in high-dimensional settings.
method A novel approximation method that works well in high dimensions, especially for sparse parameters.
result One approximation method performs well in high dimensions, with running time and error dependent on the support size.
Upper bounds for CV errors apply to lasso and other models.
problem Bounding CV errors for lasso and similar models.
method Rademacher complexity and Orlicz-Ψν norm. result Upper bounds are tight and stable for lasso.
The paper addresses errors in online selective conformal prediction and proposes new strategies to ensure valid inference.
problem Online selective conformal prediction's exchangeability issues and false coverage rate control problems.
method Evaluation and correction of existing calibration selection strategies, proposing new ones that preserve exchangeability.
result Novel calibration selection strategies ensure both selection-conditional coverage and FCR control.