We prove that perfect distributions exist when using a finite number of bits to represent the parameters of a Bayesian network. In addition, we provide an upper bound on the probability of sampling a non-perfect distribution when using a fixed number of bits for the parameters and that the upper bound approaches zero exponentially fast as one increases the number of bits. We also provide an upper bound on the number of bits needed to guarantee that a distribution sampled from a uniform Dirichlet distribution is perfect with probability greater than 1\/2.<\/p>\n","protected":false},"excerpt":{"rendered":"
We prove that perfect distributions exist when using a finite number of bits to represent the parameters of a Bayesian network. 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