Classification with Valid and Adaptive Coverage
Classification with Valid and Adaptive Coverage
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发表时间：
2020-06
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通讯作者：
Yaniv Romano;Matteo Sesia;E. Candès
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作者：
Yaniv Romano;Matteo Sesia;E. Candès
共形推理、交叉验证+和折刀+都是可以与几乎任何机器学习算法相结合的方法，以构建具有保证的边缘覆盖率的预测集。在本文中，我们开发了这些技术的专门版本的分类和无序的响应标签，除了提供边际覆盖，也完全适应复杂的数据分布，在这个意义上说，他们表现良好的近似条件覆盖相比，替代方法。我们的贡献的核心是一个新的一致性分数，我们明确证明是强大的和直观的分类问题，但其基本原则是潜在的更普遍。合成和真实的数据的实验证明了我们的理论保证的实用价值，以及所提出的方法比现有的替代品的统计优势。
Conformal inference, cross-validation+, and the jackknife+ are hold-out methods that can be combined with virtually any machine learning algorithm to construct prediction sets with guaranteed marginal coverage. In this paper, we develop specialized versions of these techniques for categorical and unordered response labels that, in addition to providing marginal coverage, are also fully adaptive to complex data distributions, in the sense that they perform favorably in terms of approximate conditional coverage compared to alternative methods. The heart of our contribution is a novel conformity score, which we explicitly demonstrate to be powerful and intuitive for classification problems, but whose underlying principle is potentially far more general. Experiments on synthetic and real data demonstrate the practical value of our theoretical guarantees, as well as the statistical advantages of the proposed methods over the existing alternatives.