Required sample size for learning sparse Bayesian networks with many variables

Details Required sample size for learning sparse Bayesian networks with many variables Required sample size for learning sparse Bayesian networks with many variables

2002-04-26

arxiv.org/abs/cs/0204052v1

Computer Science

Learning

9 pages

Scientific paper

Learning joint probability distributions on n random variables requires exponential sample size in the generic case. Here we consider the case that a temporal (or causal) order of the variables is known and that the (unknown) graph of causal dependencies has bounded in-degree Delta. Then the joint measure is uniquely determined by the probabilities of all (2 Delta+1)-tuples. Upper bounds on the sample size required for estimating their probabilities can be given in terms of the VC-dimension of the set of corresponding cylinder sets. The sample size grows less than linearly with n.

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