Book ChapterDOI
Bias in Estimating the Variance of K-Fold Cross-Validation
Yoshua Bengio,Yves Grandvalet +1 more
- pp 75-95
Reads0
Chats0
TLDR
The main theorem shows that there exists no universal (valid under all distributions) unbiased estimator of the variance of K-fold cross-validation, based on a single computation of the K- fold cross- validation estimator.Abstract:
Most machine learning researchers perform quantitative experiments to estimate generalization error and compare the perforniance of different algorithms (in particular, their proposed algorithmn). In order to be able to draw statistically convincing conclusions, it is important to estimate the uncertainty of such estimates. This paper studies the very commonly used K-fold cross-validation estimator of generalization performance. The main theorem shows that there exists no universal (valid under all distributions) unbiased estimator of the variance of K-fold cross-validation, based on a single computation of the K-fold cross-validation estimator. The analysis that accompanies this result is based on the eigen-decomposition of the covariance matrix of errors, which has only three different eigenvalues corresponding to three degrees of freedom of the matrix and three components of the total variance. This analysis helps to better understand the nature of the problem and how it can make naive estimators (that don't take into account the error correlations due to the overlap between training and test sets) grossly underestimate variance. This is confirmed by numerical experiments in which the three components of the variance are compared when the difficulty of the learning problem and the number of folds are varied.read more
Citations
More filters
Journal ArticleDOI
Sensitivity Analysis of k-Fold Cross Validation in Prediction Error Estimation
TL;DR: This paper analyzes the statistical properties, bias and variance, of the k-fold cross-validation classification error estimator (k-cv) and proposes a novel theoretical decomposition of the variance considering its sources of variance: sensitivity to changes in the training set and sensitivity to changed folds.
Journal ArticleDOI
Predicting Diabetes Mellitus With Machine Learning Techniques.
TL;DR: The results showed that prediction with random forest could reach the highest accuracy (ACC = 0.8084) when all the attributes were used and principal component analysis (PCA) and minimum redundancy maximum relevance (mRMR) was used to reduce the dimensionality.
Posted Content
Study of Deep Learning Techniques for Side-Channel Analysis and Introduction to ASCAD Database.
TL;DR: This work proposes a comprehensive study of deep learning algorithms when applied in the context of side-channel analysis and addresses the question of the choice of the hyper-parameters for the class of multi-layer perceptron networks and convolutional neural networks.
Journal ArticleDOI
Feature Selection With Harmony Search
Ren Diao,Qiang Shen +1 more
TL;DR: The proposed approach is able to escape from local solutions and identify multiple solutions owing to the stochastic nature of HS, and is compared with those that rely on HC, genetic algorithms, and particle swarm optimization.
Journal ArticleDOI
Deep learning for side-channel analysis and introduction to ASCAD database
TL;DR: This work proposes a study of deep learning algorithms when applied in the context of side-channel analysis and discusses the links with the classical template attacks, and addresses the question of the choice of the hyper-parameters for the class convolutional neural networks.
References
More filters
Book
An introduction to the bootstrap
Bradley Efron,Robert Tibshirani +1 more
TL;DR: This article presents bootstrap methods for estimation, using simple arguments, with Minitab macros for implementing these methods, as well as some examples of how these methods could be used for estimation purposes.
Proceedings Article
A study of cross-validation and bootstrap for accuracy estimation and model selection
TL;DR: The results indicate that for real-word datasets similar to the authors', the best method to use for model selection is ten fold stratified cross validation even if computation power allows using more folds.
Journal ArticleDOI
Cross-Validatory Choice and Assessment of Statistical Predictions
TL;DR: In this article, a generalized form of the cross-validation criterion is applied to the choice and assessment of prediction using the data-analytic concept of a prescription, and examples used to illustrate the application are drawn from the problem areas of univariate estimation, linear regression and analysis of variance.
Book
A Probabilistic Theory of Pattern Recognition
TL;DR: The Bayes Error and Vapnik-Chervonenkis theory are applied as guide for empirical classifier selection on the basis of explicit specification and explicit enforcement of the maximum likelihood principle.