Learning Polytrees with Constant Number of Roots from Data

  • Javad Safaei
  • Ján Maňuch
  • Ladislav Stacho
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8272)


Chow and Liu [2] has shown that learning trees that maximize likelihood score given data can be done in polynomial time. A generalization of directed trees are polytrees. However, Dasgupta [3] has proved that learning maximum likelihood polytrees from data (and even approximation of the optimal result with a constant ratio) is NPHard. Therefore, researchers have focused on learning maximum likelihood polytrees with a constant number of roots. Gaspers et al. [5] have presented such an algorithm with complexity O(mn 3k + 4) using matroid theory. We present a direct combinatorial algorithm with complexity O(mn 3k + 1).


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Javad Safaei
    • 1
  • Ján Maňuch
    • 1
    • 2
  • Ladislav Stacho
    • 2
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada
  2. 2.Department of MathematicsSimon Fraser UniversityBurnabyCanada

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