论文标题
掌握：分类学习的合适性测试
GRASP: A Goodness-of-Fit Test for Classification Learning
论文作者
论文摘要
分类器的性能通常是根据测试数据的平均准确性来衡量的。尽管是标准措施，但平均准确性未能表征模型对标签的基本条件定律的拟合度，鉴于特征向量（$ y | x $），例如由于模型错误指定，拟合和高维度。在本文中，我们考虑了评估一般二元分类器的拟合优点的基本问题。我们的框架没有对条件定律$ y | x $做出任何参数假设，并且将其视为黑匣子甲骨文模型，只能通过查询访问。我们将拟合优度评估问题提出作为表格\ [h_0：\ mathbb {e} \ big [d_f \ big（{\ sf bern}（η（x））的耐受性假设检验。 $ d_f $代表$ f $ -Divergence函数，$η（x）$，$ \hatη（x）$分别表示true和估计可能性vector $ x $的估计可能性。我们提出了一个新颖的测试，称为\ grasp用于测试$ H_0 $，无论功能如何（无分配）在有限的样品设置中起作用。我们还提出了为模型-X设置设计的Model-X \ Grasp，其中已知特征向量的关节分布。 Model-X \ Grasp使用此分配信息来实现更好的功率。我们通过广泛的数值实验评估测试的性能。
Performance of classifiers is often measured in terms of average accuracy on test data. Despite being a standard measure, average accuracy fails in characterizing the fit of the model to the underlying conditional law of labels given the features vector ($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.
