Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Advances in probabilistic reasoning
Proceedings of the seventh conference (1991) on Uncertainty in artificial intelligence
On the generation of alternative explanations with implications for belief revision
Proceedings of the seventh conference (1991) on Uncertainty in artificial intelligence
Approximating probabilistic inference in Bayesian belief networks is NP-hard
Artificial Intelligence
A linear constraint satisfaction approach to cost-based abduction
Artificial Intelligence
Finding MAPs for belief networks is NP-hard
Artificial Intelligence
On Spline Approximations for Bayesian Computations
On Spline Approximations for Bayesian Computations
A logic for semantic interpretation
ACL '88 Proceedings of the 26th annual meeting on Association for Computational Linguistics
A computational model for causal and diagnostic reasoning in inference systems
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 1
A new admissible heuristic for minimal-cost proofs
AAAI'91 Proceedings of the ninth National conference on Artificial intelligence - Volume 1
Explanation, irrelevance and statistical independence
AAAI'91 Proceedings of the ninth National conference on Artificial intelligence - Volume 1
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Independence-based (IB) assignments to Bayesian belief networks were originally proposed as abductive explanations. IB assignments assign fewer variables in abductive explanations than do schemes assigning values to all evidentially supported variables. We use IB assignments to approximate marginal probabilities in Bayesian belief networks. Recent work in belief updating for Bayes networks attempts to approximate posterior probabilities by finding a small number of the highest probability complete (or perhaps evidentially supported) assignments. Under certain assumptions, the probability mass in the union of these assignments is sufficient to obtain a good approximation. Such methods are especially useful for highly-connected networks, where the maximum clique size or the cutset size make the standard algorithms intractable. Since IB assignments contain fewer assigned variables, the probability mass in each assignment is greater than in the respective complete assignment. Thus, fewer IB assignments are sufficient, and a good approximation can be obtained more efficiently. IB assignments can be used for efficiently approximating posterior node probabilities even in cases which do not obey the rather strict skewness assumptions used in previous research. Two algorithms for finding the high probability IB assignments are suggested: one by doing a best-first heuristic search, and another by special-purpose integer linear programming. Experimental results show that this approach is feasible for highly connected belief networks.