On conditional belief functions in directed graphical models in the Dempster-Shafer theory
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Issue Date
2023-07-04Author
Jiroušek, Radim
Kratochvíl, Václav
Shenoy, Prakash P.
Publisher
Elsevier
Type
Article
Article Version
Scholarly/refereed, publisher version
Rights
© 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license.
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The primary goal is to define conditional belief functions in the Dempster-Shafer theory. We do so similarly to probability theory's notion of conditional probability tables. Conditional belief functions are necessary for constructing directed graphical belief function models in the same sense as conditional probability tables are necessary for constructing Bayesian networks. We provide examples of conditional belief functions, including those obtained by Smets' conditional embedding. Besides defining conditional belief functions, we state and prove a few basic properties of conditionals. In the belief-function literature, conditionals are defined starting from a joint belief function. Conditionals are then defined using the removal operator, an inverse of Dempster's combination operator. When such conditionals are well-defined belief functions, we show that our definition is equivalent to these definitions.
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Citation
Jiroušek, R., Kratochvíl, V., Shenoy, P.P., (2023), On conditional belief functions in directed graphical models in the Dempster-Shafer theory, International Journal of Approximate Reasoning, vol. 160, 108976, https://doi.org/10.1016/j.ijar.2023.108976
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