Integer Programming for Causal Structure Learning in the Presence of Latent Variables

• URL: http://arxiv.org/abs/2102.03129v1
• Date: Fri, 5 Feb 2021 12:10:16 GMT
• Title: Integer Programming for Causal Structure Learning in the Presence of Latent Variables
• Authors: Rui Chen, Sanjeeb Dash, Tian Gao
• Abstract summary: We propose a novel exact score-based method that solves an integer programming (IP) formulation and returns a score-maximizing ancestral ADMG for a set of continuous variables. In particular, we generalize the state-of-the-art IP model for DAG learning problems and derive new classes of valid inequalities to formalize the IP-based ADMG learning model.
• Score: 28.893119229428713
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The problem of finding an ancestral acyclic directed mixed graph (ADMG) that represents the causal relationships between a set of variables is an important area of research for causal inference. However, most of existing score-based structure learning methods focus on learning the directed acyclic graph (DAG) without latent variables. A number of score-based methods have recently been proposed for the ADMG learning, yet they are heuristic in nature and do not guarantee an optimal solution. We propose a novel exact score-based method that solves an integer programming (IP) formulation and returns a score-maximizing ancestral ADMG for a set of continuous variables. In particular, we generalize the state-of-the-art IP model for DAG learning problems and derive new classes of valid inequalities to formalize the IP-based ADMG learning model. Empirically our model can be solved efficiently for medium-sized problems and achieves better accuracy than state-of-the-art score-based methods as well as benchmark constraint-based methods.

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