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Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential families
Goutham Rajendran · Bohdan Kivva · Ming Gao · Bryon Aragam

Wed Dec 08 04:30 PM -- 06:00 PM (PST) @

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

Author Information

Goutham Rajendran (University of Chicago)

I obtained my CS PhD from UChicago. Recently, I've been actively working on causal representation learning and generative models. Some of my recent side projects were on NeRF (Computer vision) and Automatic Speech Recognition. I also have extensive competitive programming experience and a track publication record.

Bohdan Kivva (University of Chicago)
Ming Gao (the University of Chicago)
Bryon Aragam (University of Chicago)

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