  We consider the task of causal structure learning over measurement dependence
inducing latent (MeDIL) causal models. We show that this task can be framed in
terms of the graph theoretic problem of finding edge clique covers,resulting in
an algorithm for returning minimal MeDIL causal models (minMCMs). This
algorithm is non-parametric, requiring no assumptions about linearity or
Gaussianity. Furthermore, despite rather weak assumptions aboutthe class of
MeDIL causal models, we show that minimality in minMCMs implies some rather
specific and interesting properties. By establishing MeDIL causal models as a
semantics for edge clique covers, we also provide a starting point for future
work further connecting causal structure learning to developments in graph
theory and network science.
