Crossing the Validation Crisis: Cross-Validation Reduces Benchmarking Variance Surprisingly Well

Scientific machine learning reports predictive performance. It does not report whether the same prediction would survive a different draw of training data. Across $9$ chemistry benchmarks, two classifiers trained on independent bootstraps of the same training set agree on aggregate accuracy to within $1.3\text{--}4.2$ percentage points but disagree on the class label of $8.0\text{--}21.8\%$ of test molecules. We call this gap \emph{cross-sample prediction churn}. The standard parameter-side techniques (deep ensembles, MC dropout, stochastic weight averaging) do not reduce this gap; two data-side methods do. The first is $K$-bootstrap bagging, which cuts the rate $40\text{--}54\%$ on every dataset at no accuracy cost ($K{\times}$-ERM compute). The second is \emph{twin-bootstrap}, our proposal: two networks trained jointly on independent bootstraps with a sym-KL consistency loss between their predictions, which at matched $2{\times}$-ERM compute reduces churn a further median $45\%$ beyond bagging-$K{=}2$. Cross-sample prediction churn deserves a column alongside predictive performance in scientific-ML benchmark reports, because without it the parameter-side and data-side methods are indistinguishable on the metric they actually differ on.

We study the mean-squared error of $k$-fold cross-validation as a risk estimator, with particular emphasis on how its accuracy depends on the number of folds $k$. Despite the widespread use of cross-validation, principled guidance for choosing $k$ is largely absent, mainly due to the complex dependence between fold-wise error estimates. To obtain sharp and interpretable results, we focus on the majority algorithm in binary classification, a minimal yet nontrivial empirical risk minimization procedure. We provide a fine-grained analysis of its cross-validation behavior, showing that even this simple algorithm exhibits subtle and delicate phenomena for which existing theory provides loose and even vacuous bounds. Leveraging this analysis, we introduce a minimax framework for cross-validation risk estimation and prove that no empirical risk minimization algorithm can achieve an $O(1/n)$ minimax mean-squared error when the number of folds grows with the number of samples $n$; instead, a lower bound of order $Ω(\sqrt{k}/n)$ is unavoidable. Our results reveal fundamental limitations of cross-validation as a data-reuse strategy, clarify gaps and inaccuracies in prior theoretical work, and position the majority algorithm as a natural benchmark that any tight analysis of cross-validation should be able to explain.

Small-to-medium scientific datasets place machine learning pipelines under two compounding pressures. Single-run feature selection produces feature sets that change substantially under small perturbations of the training data, and any procedure that uses the same data for selection, tuning, and evaluation produces optimistically biased performance estimates. The two failure modes are routinely treated as separable, but in the regimes where scientific data live, they interact: an unstable selection inflates the variance of an already-optimistic score, and standard remedies for one rarely address the other. RobustModelMaker is a Python framework that couples bootstrap stability selection with strict nested cross-validation, performs all preprocessing and selection inside each fold, and produces a stability-tested feature subset together with a leakage-safe performance estimate. The framework supports nine algorithms across binary classification, multiclass classification, and regression. Behaviour is verified by a deterministic test suite spanning unit, performance, and reproducibility checks on three real scientific datasets comparing to three alternative selectors (ANOVA F-test, recursive feature elimination with cross-validation, and Boruta) on both predictive score and a Jaccard measure of selection stability. RobustModelMaker is competitive in score with the best alternative selector on each dataset, and occupies a position on the joint score-stability frontier that none of the alternatives match across all three task types. Two example applications, ovarian cancer biomarker discovery from the PLCO Trial and critical-temperature regression on the UCI Superconductivity Data, illustrate how the framework is used in practice and what trade-offs become visible when stability is treated as a first-class deliverable rather than an emergent property.