GRASP: a goodness-of-fit test for classification learning.

Performance of classifiers is often measured in terms of average accuracy on test data. Despite being a standard measure, average accuracy fails in characterising the fit of the model to the underlying conditional law of labels given the features vector (⁠ Y ∣ X ⁠), e.g. due to model misspecification, over fitting, and high-dimensionality. In this paper, we consider the fundamental problem of assessing the goodness-of-fit for a general binary classifier. Our framework does not make any parametric assumption on the conditional law Y ∣ X and treats that as a black-box oracle model which can be accessed only through queries. We formulate the goodness-of-fit assessment problem as a tolerance hypothesis testing of the form H 0 : E [ D f (B e r n (η (X)) ‖ B e r n (η ^ (X))) ] ≤ τ where D f represents an f -divergence function, and η (x) ⁠ , η ^ (x) ⁠ , respectively, denote the true and an estimate likelihood for a feature vector x admitting a positive label. We propose a novel test, called G oodness-of-fit with Ra ndomisation and S coring P rocedure (GRASP) for testing H 0 ⁠ , which works in finite sample settings, no matter the features (distribution-free). We also propose model-X GRASP designed for model-X settings where the joint distribution of the features vector is known. Model-X GRASP uses this distributional information to achieve better power. We evaluate the performance of our tests through extensive numerical experiments. [ABSTRACT FROM AUTHOR]