Generalized structural equations models (GSEMs) [Peters and Halpern 2021], are, as the name suggests, a generalization of structural equations models (SEMs). They can deal with (among other things) infinitely many variables with infinite ranges, which is critical for capturing dynamical systems. We provide a sound and complete axiomatization of causal reasoning in GSEMs that is an extension of the sound and complete axiomatization provided by Halpern [2000] for SEMs. Considering GSEMs helps clarify what properties Halpern's axioms capture.

Drug repositioning is an attractive cost-efficient strategy for the development of treatments for human diseases. Here, we propose an interpretable model that learns disease self-representations for drug repositioning. Our self-representation model represents each disease as a linear combination of a few other diseases. We enforce the proximity between diseases to preserve the geometric structure of the human phenome network - a domain-specific knowledge that naturally adds relational inductive bias to the disease self-representations. We prove that our method is globally optimal and show results outperforming state-of-the-art drug repositioning approaches. We further show that the disease self-representations are biologically interpretable.