Probabilistic reasoning in intelligent systems: networks of plausible inference
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Finding optimal bayesian networks
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Large-sample learning of bayesian networks is NP-hard
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We consider the task of learning the maximum-likelihood polytree from data. Our first result is a performance guarantee establishing that the optimal branching (or Chow-Liu tree), which can be computed very easily, constitutes a good approximation to the best polytree. We then show that it is not possible to do very much better, since the learning problem is NP-hard even to approximately solve within some constant factor.