Probabilistic Deduction with Conditional Constraints over Basic Events

Details Probabilistic Deduction with Conditional Constraints over Basic Events Probabilistic Deduction with Conditional Constraints over Basic Events

2011-05-27

arxiv.org/abs/1105.5461v1

Journal Of Artificial Intelligence Research, Volume 10, pages 199-241, 1999

Computer Science

Artificial Intelligence

Scientific paper

10.1613/jair.577

We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NP-hard. We then concentrate on the special case of probabilistic deduction in conditional constraint trees. We elaborate very efficient techniques for globally complete probabilistic deduction. In detail, for conditional constraint trees with point probabilities, we present a local approach to globally complete probabilistic deduction, which runs in linear time in the size of the conditional constraint trees. For conditional constraint trees with interval probabilities, we show that globally complete probabilistic deduction can be done in a global approach by solving nonlinear programs. We show how these nonlinear programs can be transformed into equivalent linear programs, which are solvable in polynomial time in the size of the conditional constraint trees.

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