D. Rusakov and D. Geiger. On the parameter priors for discrete DAG models. In AI/Stats, 2001. Home/Search Document Details and Download
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Learning Bayes net structure from sparse data sets - Murphy (2001) (3 citations) (Correct)
....[SL90] We will give the form of this posterior below. Note that, if we have missing data, the parameter posterior will no longer be factored. Hence assuming parameter independence is equivalent to assuming that one s prior knowledge was derived from a fully obsered virtual database . GH97, RG01] prove that the assumptions of global and local parameter independence, plus an additional assumption called likelihood equivalence 5 , imply that the prior must be Dirichlet. Fortunately, the Dirichlet prior is the conjugate prior for the multinomial [Ber85] which makes analysis easier, as we ....
D. Rusakov and D. Geiger. On the parameter priors for discrete DAG models. In AI/Stats, 2001.
On Parameter Priors for Discrete DAG Models - Rusakov, Geiger (2000) (1 citation) Self-citation (Rusakov Geiger) (Correct)
....C is a normalization constant. The set A 0 is the set of all binary vectors of length n with even number of ones and the set A 1 is the set of all binary vectors of length n with an odd number of ones . The full proof, based on Lemmas 2 and 3, is explicated in the full version of this paper [10]. 5 Dirichlet Priors: The Minimal Set of Assumptions We have shown in the previous sections that global parameter independence alone is not enough to ensure a Dirichlet prior on the network parameters. The natural question is: What is a minimal set of independence requirements that ensure ....
....binary variables) However, the explicit general formula for such priors is not compact due to a large number of variables involved. Instead, we have developed a procedure (based on Lemmas 2 and 3) to specify such distribution (in symbolic form) for any specific DAG model (not described here, see [10]) All the results presented in this paper were achieved under the assumption of local parameter distributions being twice differentiable and everywhere positive. One may hope to derive the properties of twice differentiability and being everywhere positive for probability density functions of ....
D. Rusakov and D. Geiger. On parameter priors for discrete dag models. Technical Report CIS2000 -08, Technion, 2000.
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