DAG Learning on the Permutahedron

Valentina Zantedeschi, Luca Franceschi, Jean Kaddour, Matt Kusner, Vlad Niculae

Keywords: directed acyclic graph, causal discovery, differentiable sorting

TL;DR: We propose a continuous optimization framework over the Permutahedron for discovering (DAGs) from observations that does not relax acyclicity and accommodates any edge-optimization procedure, edge structural parameterization, and optimization loss

Abstract: We propose a continuous optimization framework for discovering a latent directed acyclic graph (DAG) from observational data. Our approach optimizes over the polytope of permutation vectors, the so-called Permutahedron, to learn a topological ordering. Edges can be optimized jointly, or learned conditional on the ordering via a non-differentiable subroutine. Compared to existing continuous optimization approaches our formulation has a number of advantages including: 1. validity: optimizes over exact DAGs as opposed to other relaxations optimizing approximate DAGs; 2. modularity: accommodates any edge-optimization procedure, edge structural parameterization, and optimization loss; 3. end-to-end: either alternately iterates between node-ordering and edge-optimization, or optimizes them jointly; We demonstrate, on real-world data problems in protein-signaling and transcriptional network discovery, that our approach lies on the Pareto frontier of two key metrics, the SID and SHD.

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