What is an optimal value of k in k-fold cross-validation in discrete Bayesian network analysis?

• Published in: Computational statistics Vol. 36; no. 3; pp. 2009 - 2031
• Main Authors: Marcot, Bruce G., Hanea, Anca M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021; Springer Nature B.V
• Subjects: Bayesian analysis; Bias; Calibration; Classification; Collinearity; Datasets; Economic Theory/Quantitative Economics/Mathematical Methods; Independent variables; Mathematics and Statistics; Network analysis; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistical methods; Statistics; Variables; Classification error; randomized subsets; sample size; Model validation
• DOI: 10.1007/s00180-020-00999-9
• ISSN: 0943-4062

Cross-validation using randomized subsets of data—known as k-fold cross-validation—is a powerful means of testing the success rate of models used for classification. However, few if any studies have explored how values of k (number of subsets) affect validation results in models tested with data of known statistical properties. Here, we explore conditions of sample size, model structure, and variable dependence affecting validation outcomes in discrete Bayesian networks (BNs). We created 6 variants of a BN model with known properties of variance and collinearity, along with data sets of n = 50, 500, and 5000 samples, and then tested classification success and evaluated CPU computation time with seven levels of folds (k = 2, 5, 10, 20, n − 5, n − 2, and n − 1). Classification error declined with increasing n, particularly in BN models with high multivariate dependence, and declined with increasing k, generally levelling out at k = 10, although k = 5 sufficed with large samples (n = 5000). Our work supports the common use of k = 10 in the literature, although in some cases k = 5 would suffice with BN models having independent variable structures.