Doubly Robust Kernel Statistics for Testing Distributional Treatment Effects
Abstract: With the widespread application of causal inference, it is increasingly important to have tools which can test for the presence of causal effects in a diverse array of circumstances. In this vein we focus on the problem of testing for \emph{distributional} causal effects, where the treatment affects not just the mean, but also higher order moments of the distribution, as well as multidimensional or structured outcomes. We build upon a previously introduced framework, Counterfactual Mean Embeddings, for representing causal distributions within Reproducing Kernel Hilbert Spaces (RKHS) by proposing new, improved, estimators for the distributional embeddings. These improved estimators are inspired by doubly robust estimators of the causal mean, using a similar form within the kernel space. We analyse these estimators, proving they retain the doubly robust property and have improved convergence rates compared to the original estimators. This leads to new permutation-based tests for distributional causal effects, by constructing the test statistics based on the estimators we propose. We experimentally and theoretically demonstrate the validity of our tests.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Bryon_Aragam1
Submission Number: 1853
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