论文标题
使用共形预测和加权等级总和的两样本条件分配测试
A Two-Sample Conditional Distribution Test Using Conformal Prediction and Weighted Rank Sum
论文作者
论文摘要
我们考虑了两个人群之间的协变量向量测试响应变量的条件分布平等的问题。这样的假设检验问题可以从各种机器学习和统计推断情景（包括转移学习和因果预测推断）中促进。我们开发了一个非参数测试程序，该程序灵感来自共形预测框架。我们的测试统计量的构建结合了共形预测中的最新发展与一种新颖的合格评分选择，从而产生了加权的等级和测试统计量，在一般环境下是有效且强大的。据我们所知，这是使用保形预测来测试超出交换性的统计假设的首次成功尝试。我们的方法适用于现代机器学习方案，在该方案中，数据具有很高的维度和大型样本量，并且可以与现有的分类算法有效结合，以找到良好的合格分数功能。在各种数值示例中证明了该方法的性能。
We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and statistical inference scenarios, including transfer learning and causal predictive inference. We develop a nonparametric test procedure inspired from the conformal prediction framework. The construction of our test statistic combines recent developments in conformal prediction with a novel choice of conformity score, resulting in a weighted rank-sum test statistic that is valid and powerful under general settings. To our knowledge, this is the first successful attempt of using conformal prediction for testing statistical hypotheses beyond exchangeability. Our method is suitable for modern machine learning scenarios where the data has high dimensionality and large sample sizes, and can be effectively combined with existing classification algorithms to find good conformity score functions. The performance of the proposed method is demonstrated in various numerical examples.
