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Greedy Causal Discovery is Geometric · Around

2021

Greedy Causal Discovery is Geometric

Linusson, Svante, Restadh, Petter, Solus, Liam

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Finding a directed acyclic graph (DAG) that best encodes the conditional independence statements observable from data is a central question within causality.

Algorithms that greedily transform one candidate DAG into another given a fixed set of moves have been particularly successful, for example the GES, GIES, and MMHC algorithms.
In 2010, Studen\'y, Hemmecke and Lindner introduced the characteristic imset polytope, $\operatorname{CIM}_p$, whose vertices correspond to Markov equivalence classes, as a way of transforming causal discovery into a linear optimization problem.
We show that the moves of the aforementioned algorithms are included within classes of edges of $\operatorname{CIM}_p$ and that restrictions placed on the skeleton of the candidate DAGs correspond to faces of $\operatorname{CIM}_p$.

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