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Greedy algorithms have long been a workhorse for learning graphical models,and more broadly for learning statistical models with sparse structure. In thecontext of learning directed acyclic graphs, greedy algorithms are populardespite their worst-case exponential runtime. In practice, however, they arevery efficient. We provide new insight into this phenomenon by studying ageneral greedy score-based algorithm for learning DAGs. Unlike edge-greedyalgorithms such as the popular GES and hill-climbing algorithms, our approachis vertex-greedy and requires at most a polynomial number of score evaluations.We then show how recent polynomial-time algorithms for learning DAG models area special case of this algorithm, thereby illustrating how these order-basedalgorithms can be rigourously interpreted as score-based algorithms. Thisobservation suggests new score functions and optimality conditions based on theduality between Bregman divergences and exponential families, which we explorein detail. Explicit sample and computational complexity bounds are derived.Finally, we provide extensive experiments suggesting that this algorithm indeedoptimizes the score in a variety of settings.

Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential families