Causal invariance in graphical models with latent variables

M. Borriero${}^a$, M. Lupparelli${}^a$, G. M. Marchetti${}^a$ and V. Vinciotti${}^b$

${}^a$Department of Statistics, Computer Science and Applications, University of Florence, ${}^b$Department of Mathematics, University of Trento

The purpose of causal discovery is to identify causal relationships among variables from observational or interventional data, typically represented by a directed acyclic graph (DAG). In [1] the authors introduced the invariant causal prediction methodology that enables the identification of the causal parents of target variables by exploiting the stability of causal effects across different experimental settings. However, when some parents are unobserved, the induced graph over the observed variables may no longer be a DAG. In fact, in general it belongs to a broader class of graphs, and moreover it may not be unique, complicating causal inference. We examine in detail relevant configurations of latent parents, with particular attention to the case of hidden confounders, we characterize the induced graph and formalize the conditions under which causal invariance is preserved for identification of the observed parents. Necessary and sufficient conditions for testing such invariance are formally established for a (multivariate) Gaussian target.

Keywords: acyclic directed mixed graphs; identifiability; mediation analysis.