Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential families
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, th...
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| Main Authors | , , , |
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| Format | Journal Article |
| Language | English |
| Published |
10.10.2021
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2110.04719 |
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| Summary: | 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. |
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| DOI: | 10.48550/arxiv.2110.04719 |