Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression
This work addresses the limitation of focusing only on average effects in causal inference, offering a method to assess full distributional impacts, though it is incremental as it builds on existing kernel and U-statistic techniques.
The authors tackled the problem of analyzing treatment effects beyond the mean by proposing the conditional distributional treatment effect (CoDiTE), which encodes distributional aspects using kernel conditional mean embeddings and U-statistic regression, with experiments on synthetic and real datasets showing its effectiveness.
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.