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On the Complexity of Belief Network Synthesis and Refinement (1992)  (Make Corrections)  (1 citation)
Marco Valtorta, Donald W. Loveland



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Abstract: This paper addresses the problem of synthesis and refinement of numerical parameters in belief networks from an algorithmic standpoint. Both Dempster-Shafer networks and Bayesian networks are considered. Section 2 formalizes the problem already described in this introduc- tion, by using the notion of case, in the Dempster-Shafer framework. Section 3 shows that the synthesis of masses in Dempster-Shafer networks from cases is NP-hard. Section 4 is devoted to the proof that the refinement of... (Update)

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...first chapter of Pearl s book [Pearl, 1988] for a discussion of the tradeoff between complexity and soundness. See also [Wang and Valtorta, 1992] for a specific example of this tradeoff. To prove a refinement problem is NP hard or polynomially solvable, a particular set of...

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BibTeX entry:   (Update)

Valtorta, M. and Loveland, D. (1992). On the complexity of belief network synthesis and refinement. International Journal of Approximate Reasoning, 7(3--4). http://citeseer.ist.psu.edu/valtorta92complexity.html   More

@misc{ valtorta92complexity,
  author = "M. Valtorta and D. Loveland",
  title = "the complexity of belief network synthesis and refinement",
  text = "Valtorta, M. and Loveland, D. (1992). On the complexity of belief network
    synthesis and refinement. International Journal of Approximate Reasoning,
    7(3--4).",
  year = "1992",
  url = "citeseer.ist.psu.edu/valtorta92complexity.html" }
Citations (may not include all citations):
1543   Probabilistic Reasoning in Intelligent Systems: Networks of .. (context) - Pearl - 1988
582   Local Computations with Probabilities on Graphical Struc- tu.. (context) - Lauritzen, Spiegelhalter - 1988
90   Neural Network Design and the Complexity of Learning (context) - Judd - 1990
67   Subjective Bayesian Methods for Rule-Based Inference Systems (context) - Duda, Hart et al. - 1976
61   Bayesian and Non-Bayesian Evidential Updating (context) - Kyburg - 1987
51   Belief Functions (context) - Smets - 1988
49   MUNIN--A Causal Probabilistic Network for Interpretation of .. (context) - Andreassen, Woldbye et al. - 1987
49   Probabilistic Inference Using Belief Networks is NP-hard (context) - Cooper - 1987
32   Training a 3-Node Neural Network is NP-Complete (context) - Blum, Rivest - 1988
23   A Method for Managing Evidential Reasoning in a Hierarchical.. (context) - Gordon, Shortliffe - 1985
18   Propagating Belief Functions in Qualitative Markov Trees (context) - Shafer, Shenoy et al. - 1987
14   Propagating Belief Functions with Local Computations (context) - Shenoy, Shafer - 1986
12   Learning in Neural Networks (context) - Judd - 1988
10   An Axiomatic Framework for Bayesian and Belief-function Prop.. (context) - Shenoy, Shafer - 1988
9   Complexity of Connectionist Learning with Various Node Funct.. (context) - Judd - 1987
7   A Logic-Based Analysis of Dempster-Shafer Theory (context) - Provan - 1990
7   Multivariate Belief Functions and Graphical Models (context) - Kong - 1986
7   The Elements of Artificial Intelligence Using Common LISP (context) - Tanimoto - 1990
7   Computers and lntractability: A Guide to the Theory of NP- C.. (context) - Garey, Johnson - 1979
6   the Propagation of Beliefs in Networks Using the Dempster-Sh.. (context) - Mellouli - 1988
6   Adapting Connectionist Learning to Bayes Networks (context) - Laskey - 1990
4   Some Results on Knowledge Base Refinement with an Oracle (context) - Valtorta - 1989
3   Complexity Issues in Learning by Neural Nets (context) - Lin - 1989
3   On Debugging Rule Sets When Reasoning Under Uncertainty (context) - Wilkins, Buchanan - 1986
3   Dempster's Rule of Combination is # P-Complete - Orponen - 1990
3   Automating Rule Strengths in Expert Systems (context) - Valtorta - 1987
3   Truth Maintenance Under Uncertainty (context) - Fu - 1988
3   Some Results on the Computational Complexity of Refining Con.. - Valtorta - 1991
2   Machine Learning: Proceedings of the Sixth International Wor.. (context) - Segre - 1989
2   An Evidential Reasoning System (context) - Zarley - 1988
1   Soliciting Weights or Probabilities from Experts for Rule-Ba.. (context) - O'Leary - 1990
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