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arXiv 2102.08208stat.MLcs.LG
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基于核条件均值嵌入和U-统计量回归的条件分布处理效应

Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression

Max Planck Institute for Intelligent Systems(马克斯·普朗克智能系统研究所);Technion, Israel Institute of Technology(以色列理工学院)

Junhyung Park, Uri Shalit, Bernhard Schölkopf, Krikamol Muandet

摘要:

我们建议分析的条件分布处理效应(CoDiTE),这与更常见的条件平均处理效应(CATE),是设计来编码治疗的分布方面超出了平均值。我们首先介绍一个正式的定义与概率测度之间的距离函数的CoDiTE。然后,我们通过内核条件均值嵌入,再加上假设检验,告诉我们是否有任何条件的分布效应的治疗,讨论了与最大均值差异相关的CoDiTE。最后,我们调查了什么样的条件分布效应的治疗,无论是在探索性的方式通过条件见证函数,并通过U-统计回归的定量方式,概括的CATE高阶矩。在合成、半合成和真实数据集上的实验证明了该方法的优点。

英文摘要:

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.

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