Equivalence testing and run-count design for stochastic machine-learning experiments

Dmytro Knopov, Nadiya Shvai

Claims that two training methods perform equally well often rest on a non-significant difference between two or three runs per method. We develop a protocol, with its power theory, for certifying practical equivalence in per-run metrics such as the AUROC (area under the receiver operating characteristic curve). It rests on a two-level (seed x item) variance model separating between-run dispersion from item-level noise. Equivalence within a pre-specified margin is tested by two one-sided tests (TOST), equivalently by a confidence interval inside the margin; a two-level bootstrap covers composite statistics. A closed-form formula converts a margin and a target power into runs per method; its shifted-t refinement is calibrated against the realised two-level process. Simulations on a 270-cell grid and under non-Gaussian seed laws confirm the formula within its design-relevant range, from five runs per method. For four published runs of a joint energy-based model, the failure to certify equivalence was largely decided by design: with the variance calibrated to those runs, two per method certify with probability near three per cent, whereas certifying 0.01 AUROC at 80 per cent power…