Comment on "Causal inference using invariant prediction"
We congratulate the authors on this thought provoking paper. Statistical inference of causality has been thoroughly studied in randomized experiments or observational studies, but is seldom considered when data from both observational and interventional settings are available. Peters et al. made an important contribution by tackling this problem with their notion of invariant causal prediction (ICP) At first look, ICP is a corollary of structural equation models, but we think its value might be much more substantial. Dawid [2000] noticed that causal researchers are predominately Laplacian determinists, for who "nothing short of a functional model relating outputs to inputs will do as a description of nature" Peters et al. provide an alternative approach that defines causality by predictability instead of determinism, two different concepts that are not logically connected [Hoefer, 2016] In light of Breiman [2001]'s two cultures of statistics, determinism roughly corresponds to the data modeling culture and predictability is the spirit of Breiman's algorithmic modeling culture. Bearing this difference in mind, Peters et al. do not take a downright predictability approach in this paper. Rather, they consider two types of assumptions: invariant prediction in order to define causality and deterministic modeling assumptions such as linearity. This hybrid perspective becomes clear when comparing the assumptions in Equation (4) to (24) (28) or (31) As a consequence, ICP is able to make causal discovery only when the modeling assumptions are correct. The authors take this as a robustness property, but in our view it also limits the applicability in practice. We did not find in the paper a summary of the robustness of ICP, so we tried to outline in Table 1 the behavior of linear ICP when some of its assumptions are not met. We would welcome the authors' comments on this summary. To test the empirical performance of ICP, we use the authors' software on a protein signaling network dataset. Sachs et al. [2005] collected a combination of observational and 9 interventional datasets to infer the causal structure of 11 *Correspondence address: qyzhao@stanford.edu +Contributed equally.