Measurement Dependence Inducing Latent Causal Models

TL;DR

This paper introduces a non-parametric method for learning latent causal structures based on measurement dependence, utilizing graph theory concepts like edge clique covers to identify minimal models without assuming linearity or Gaussianity.

Contribution

It formulates causal structure learning as an edge clique cover problem, providing a novel algorithm for minimal MeDIL causal models with specific properties.

Findings

Algorithm for minimal MeDIL causal models (minMCMs)

No assumptions about linearity or Gaussianity needed

Establishes a connection between causal models and graph theory

Abstract

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.