Nonlinear Causal Discovery via Kernel Anchor Regression

Causal relationships are concerned with consequences of actions or decisions; thus, understanding these relationships can be the key ingredient in many scientific studies. For instance, medical practitioners need to know whether a treatment is effective to the target disease in clinical trials; econometricians ask whether a particular purchasing behaviour drives a change in Consumer Price Index (CPI); epidemiologists want to understand whether a government intervention policy has a positive effect on the pandemic. While the goal of revealing causal effects remains the same, the focus in causal relationships can differ by applications. To describe different aspects of the causal notion and design statistical procedures for inferring causal effects, various frameworks have been developed including Rubin's potential outcome framework [Rubin, 2004, 2005], counterfactual distributions [Chernozhukov et al., 2013] and Pearl's causal graphical models [Pearl et al., 2000, 2016]. A succinct yet comprehensive introduction can be found in Peters et al. [2017]. Causality has also been an evolving field in machine learning community and machine learning techniques have been considered to improve the statistical procedures for causal discovery. In particular, nonparmetric independence [Gretton et al., 2005] and conditional independence [Fukumizu et al., 2007] measures have been exploited to infer causal graphical models [Colombo