We propose to analyse the conditional distributional treatment effect (CoDiTE), which, in contrast to the more common conditional average treatment effect (CATE), is designed to encode a treatment's distributional aspects beyond the mean. We first introduce a formal definition of the CoDiTE associated with a distance function between probability measures. Then we discuss the CoDiTE associated with the maximum mean discrepancy via kernel conditional mean embeddings, which, coupled with a hypothesis test, tells us whether there is any conditional distributional effect of the treatment. Finally, we investigate what kind of conditional distributional effect the treatment has, both in an exploratory manner via the conditional witness function, and in a quantitative manner via U-statistic regression, generalising the CATE to higher-order moments. Experiments on synthetic, semi-synthetic and real datasets demonstrate the merits of our approach.

翻译：我们建议分析有条件分配治疗效果(CoDiTE),这一效果与更常见的有条件平均治疗效果(CATE)形成对照,旨在将治疗的分布方面编码为超出平均值。我们首先对与概率测量之间的距离函数相关的CoDiTE正式下定义。然后我们讨论与通过内核有条件平均嵌入的最大平均差异相关的CoDiTE相关联的CoDiTE, 加上一项假设测试,告诉我们治疗是否有任何有条件的分布效果。最后,我们调查该治疗通过有条件证人功能的探索性方式,以及通过U-统计回归的定量方式,将CATE概括到更高层次的时刻,对合成、半合成和真实数据集的实验证明了我们的方法的优点。