GRASP: A Goodness-of-Fit Test for Classification Learning
This addresses model misspecification and overfitting in classification for machine learning practitioners, offering a more robust evaluation method, though it is incremental as it builds on existing hypothesis testing frameworks.
The paper tackles the problem of assessing goodness-of-fit for binary classifiers beyond average accuracy, proposing GRASP tests that work in finite samples without parametric assumptions, with model-X GRASP showing improved power when feature distributions are known.
Performance of classifiers is often measured in terms of average accuracy on test data. Despite being a standard measure, average accuracy fails in characterizing 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 \[ H_0: \mathbb{E}\Big[D_f\Big({\sf Bern}(η(X))\|{\sf Bern}(\hatη(X))\Big)\Big]\leq τ\,, \] where $D_f$ represents an $f$-divergence function, and $η(x)$, $\hatη(x)$ respectively denote the true and an estimate likelihood for a feature vector $x$ admitting a positive label. We propose a novel test, called \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.