andaccuracy

Andaccuracy is a neologism used in discussions of model evaluation and ensemble methods to denote a composite metric that reflects the probability that several predictions are simultaneously correct. It is not a widely standardized term and appears primarily in informal discussions or methodological papers exploring intersection-level performance in ensembles.

Formal definition: If k classifiers produce predictions on the same set of instances, and each classifier has an accuracy ai on a held-out test set, the andaccuracy is the probability that all k classifiers are correct on a randomly chosen instance. When the predictions are assumed independent, this probability equals the product A_and = ∏_{i=1}^k ai. In cases with correlated errors, A_and must be estimated from data and may differ from the product of margins.

Example: with two classifiers having accuracies 0.9 and 0.8 and independent errors, the andaccuracy is 0.72, meaning 72% of instances are correctly classified by both classifiers.

Relation to other metrics and uses: Andaccuracy differs from standard accuracy, which measures the fraction of instances where an ensemble is correct under a chosen aggregation rule or where at least one component is correct. Andaccuracy is particularly relevant for systems that require unanimous agreement, such as high-stakes or error-sensitive applications, or to assess the joint reliability of independent components. Limitations include strong sensitivity to individual component performance and the independence assumption; in practice, correlations must be accounted for.

See also: accuracy, ensemble learning, joint probability, intersection probability.