Uncertainty in Artificial Intelligence
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Saturated Conditional Independence with Fixed and Undetermined Sets of Incomplete Random Variables
Henning Koehler, Sebastian Link
Abstract:
The implication problem for saturated condi- tional independence statements is studied in the presence of fixed and undetermined sets of in- complete random variables. Here, random vari- ables are termed incomplete since they admit missing data. Two different notions of implica- tion arise. In the classic notion of V -implication, a statement is implied jointly by a set of state- ments and a fixed set V of random variables. In the alternative notion of pure implication, a statement is implied by a given set of state- ments alone, leaving the set of random vari- ables undetermined. A first axiomatization for V -implication is established that distinguishes purely implied from V -implied statements. Ax- iomatic, algorithmic and logical characteriza- tions of pure implication are established. Pure implication appeals to applications in which the existence of random variables is uncertain, for example, when independence statements are in- tegrated from different sources, when random variables are unknown or shall remain hidden.
Keywords:
Pages: 410-419
PS Link:
PDF Link: /papers/14/p410-koehler.pdf
BibTex:
@INPROCEEDINGS{Koehler14,
AUTHOR = "Henning Koehler and Sebastian Link",
TITLE = "Saturated Conditional Independence with Fixed and Undetermined Sets of Incomplete Random Variables",
BOOKTITLE = "Proceedings of the Thirtieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-14)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2014",
PAGES = "410--419"
}


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