Exact and Approximate Algorithms for Polytree Learning
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914530888515584 |
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| author | Harviainen, Juha Sommer, Frank Sorge, Manuel |
| author_facet | Harviainen, Juha Sommer, Frank Sorge, Manuel |
| contents | Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the problem of learning the best polytree is NP-hard, we study which restrictions make it more tractable by considering for example in-degree bounds, properties of score functions measuring the quality of a polytree, and approximation algorithms. We devise an algorithm that finds the optimal polytree in time $O((2+ε)^n)$ for arbitrarily small $ε> 0$ and any constant in-degree bound $k$, improving over the fastest previously known algorithm of time complexity $O(3^n)$. We further give polynomial-time algorithms for finding a polytree whose score is within a factor of $k$ from the optimal one for arbitrary scores and a factor of $2$ for additive ones. Many of the results are complemented by (nearly) tight lower bounds for either the time complexity or the approximation factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03622 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact and Approximate Algorithms for Polytree Learning Harviainen, Juha Sommer, Frank Sorge, Manuel Data Structures and Algorithms Computational Complexity Machine Learning Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the problem of learning the best polytree is NP-hard, we study which restrictions make it more tractable by considering for example in-degree bounds, properties of score functions measuring the quality of a polytree, and approximation algorithms. We devise an algorithm that finds the optimal polytree in time $O((2+ε)^n)$ for arbitrarily small $ε> 0$ and any constant in-degree bound $k$, improving over the fastest previously known algorithm of time complexity $O(3^n)$. We further give polynomial-time algorithms for finding a polytree whose score is within a factor of $k$ from the optimal one for arbitrary scores and a factor of $2$ for additive ones. Many of the results are complemented by (nearly) tight lower bounds for either the time complexity or the approximation factors. |
| title | Exact and Approximate Algorithms for Polytree Learning |
| topic | Data Structures and Algorithms Computational Complexity Machine Learning |
| url | https://arxiv.org/abs/2605.03622 |