Is K-fold cross validation the best model selection method for machine learning?

As a technique that can compactly represent complex patterns, machine learning has significant potential for predictive inference in multi-source and heterogeneous information fusion scenarios. K-fold cross-validation (CV) is the most common approach for ascertaining the likelihood that a machine learning outcome is generated by chance and frequently outperforms conventional hypothesis testing. This improvement arises from measures directly obtained from machine learning classifications, such as accuracy, that do not have a parametric description. To approach a frequentist analysis within fusion-oriented machine learning pipelines, a permutation test or simple statistics from data partitions (i.e., folds) can be added to estimate confidence intervals. Unfortunately, neither parametric nor non-parametric tests solve the inherent problems of partitioning small sample-size datasets and learning from heterogeneous fused data sources. The fact that machine learning strongly depends on the learning parameters and the distribution of data across folds recapitulates familiar difficulties around excess false positives, uncertainty propagation, and replication. A novel statistical test based on K-fold CV and the Upper Bound of the actual risk (K-fold CUBV) is proposed, where uncertain predictions of machine learning with CV are bounded by the worst case through the evaluation of concentration inequalities. Probably Approximately Correct–Bayesian upper bounds for linear classifiers in combination with K-fold CV are derived and used to estimate the actual risk. Additionally, the origins of the replication problem are demonstrated by modeling and simulating common experimental circumstances, including small sample sizes, low numbers of predictors, and multi-source data heterogeneity. The performance with simulated and neuroimaging datasets suggests that K-fold CUBV is a robust procedure for detecting effects and validating accuracy values obtained from machine learning and classical CV schemes, while avoiding excess false positives in fusion-based inference contexts.