Dempsterian-Shaferian Belief Network From Data
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Shenoy and Shafer Shenoy:90 demonstrated that both for Dempster-Shafer Theory and probability theory there exists a possibility to calculate efficiently marginals of joint belief distributions (by so-called local computations) provided that the joint distribution can be decomposed (factorized) into a belief network. A number of algorithms exists for decomposition of probabilistic joint belief distribution into a bayesian (belief) network from data. For example Spirtes, Glymour and ScheinSpirtes:90b formulated a Conjecture that a direct dependence test and a head-to-head meeting test would suffice to construe bayesian network from data in such a way that Pearl's concept of d-separation Geiger:90 applies. This paper is intended to transfer Spirtes, Glymour and Scheines Spirtes:90b approach onto the ground of the Dempster-Shafer Theory (DST). For this purpose, a frequentionistic interpretation of the DST developed in Klopotek:93b is exploited. A special notion of conditionality for DST is introduced and demonstrated to behave with respect to Pearl's d-separation Geiger:90 much the same way as conditional probability (though some differences like non-uniqueness are evident). Based on this, an algorithm analogous to that from Spirtes:90b is developed. The notion of a partially oriented graph (pog) is introduced and within this graph the notion of p-d-separation is defined. If direct dependence test and head-to-head meeting test are used to orient the pog then its p-d-separation is shown to be equivalent to the Pearl's d-separation for any compatible dag.
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