We consider the task of causal structure learning over a set of measurement variables with no direct causal relations and whose dependencies are induced by unobserved latent variables. We call this the \textit{measurement dependence inducing latent} (MeDIL) Causal Model, or MCM, framework. We show that this task can be framed in terms of the graph theoretical problem of finding edge clique covers, resulting in a simple algorithm for returning minimal MeDIL causal models (minMCMs). This algorithm is non-parametric, requiring no assumptions about linearity or Gaussianity. Furthermore, despite these rather weak and general assumptions, we are able to show that \textit{minimality} in minMCMs implies three rather specific and interesting properties: first, minMCMs lower bound (i) the number of latent causal variables and (ii) the number of functional causal relations that are required to model a complex system at \textit{any} level of granularity; second, a minMCM contains no causal links between the latent variables; and third, in contrast to factor analysis, a minMCM may require more latent than measurement variables.

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