This Article 
 Bibliographic References 
 Add to: 
Causal Probabilistic Networks with Both Discrete and Continuous Variables
March 1993 (vol. 15 no. 3)
pp. 275-279

An extension of the expert system shell known as handling uncertainty by general influence networks (HUGIN) to include continuous variables, in the form of linear additive normally distributed variables, is presented. The theoretical foundation of the method was developed by S.L. Lauritzen, whereas this report primarily focus on implementation aspects. The approach has several advantages over purely discrete systems. It enables a more natural model of of the domain in question, knowledge acquisition is eased, and the complexity of belief revision is most often reduced considerably.

[1] S. K. Andersen, K. G. Olesen, F. V. Jensen, and F. Jensen, "HUGIN--A shell for building belief universes for expert systems," inProc. 11th Int. Joint Conf. Artificial Intell., 1989, pp. 1080-1085.
[2] S. Andreassen, B. Falck, and K. G. Olesen, "Diagnostic function of the microhuman prototype of the expert system MUNIN,"Electroencephalog Clinical Neurophys., vol. 85, pp. 143-157, 1992.
[3] S. Andreassenet al., "MUNIN--An EMG assistant," inComputer-Aided Surface Needle Electromyography Expert Systems in Diagnosis(J.E. Desmedt, Ed.). Amsterdam: Elsevier, 1989.
[4] S. Andreassen, A. Rosenfalck, B. Falck, K. G. Olesen, and S. K. Andersen, "Evaluation of the diagnostic performance of the expert EMG assistant MUNIN," to be published.
[5] S. Andreassen, M. Woldbye, B. Falck, and S. K. Andersen, "MUNIN--A causal probabilistic network for interpretation of electromyographic findings," inProc. 10th Int. Joint Conf. Artificial Intell, 1987, pp. 366-372.
[6] R. Bellazzi, S. Quaglini, C. Berzuini, and M. Stefanelli, "GAMEES: A probabilistic environment for expert systems,"Comput. Methods Programs Biomed., vol. 35, pp. 177-191, 1991.
[7] G. F. Cooper, "The computational complexity of probabilistic inference using Bayesian belief networks,"Artificial Intell., vol. 42, nos. 2-3, pp. 393-405, 1990.
[8] G. Forsythe and C. B. Moler,Computer Solution of Linear Algebra Systems. Englewood Cliffs, NJ: Prentice Hall, 1967.
[9] A. J. Gammerman, C. G. G. Aitken, Z. Luo, and M. Talbot, "A computational system for mixed probabilistic models," to be published.
[10] F. V. Jensen, "Junction trees and decomposable hypergraphs," Judex Res. Rep., Aalborg, Denmark, 1988.
[11] F. V. Jensen, S. L. Lauritzen, and K. G. Olesen, "Bayesian updating in causal probalistic networksby local computations,"Comput. Stat. Quar., vol. 4, pp. 269-282, 1990,
[12] F. V. Jensen, K. G. Olesen, and S. K. Andersen, "An algebra of Bayesian belief universes for knowledge based systems,"Networksvol. 20, pp. 637-659, 1990.
[13] U. Kjærulff, "Triangulation of graphs--Algorithms giving small total clique size," Res. Rep. R 90-09, Inst. Electron. Syst., Aalborg Univ., 1990.
[14] S. L. Lauritzen, "Propagation of probabilities, means and variances in mixed graphical association models,"J. Amer. Stat. Assoc., to be published.
[15] S. L. Lauritzen, and D. J. Spiegelhalter, "Local computations with probabilities on graphical structures and their application to expert systems (with discussion),"J. Royal Stat. Soc., Series B, vol. 50, pp. 157-224, 1988.
[16] S. L. Lauritzen and N. Wermuth, "Graphical models for associations between variables, some of which are qualitative and some quantitative,"Ann. Stat., vol. 17, pp. 31-57, 1989.
[17] H.-G. Leimer, "Triangulated graphs with marked vertices," inGraph Theory in Memory of G. A. Dirac(L. D. Andersenet al., Eds.).Annals of Discrete Mathematics, 1989, pp. 311-324, vol. 41.
[18] K. G. Olesenet al., "A MUNIN network for the median nerve--A case study on loops,"Applied Artificial Intell., vol. 3, pp. 385-404, 1989.
[19] J. Pearl, "Fusion, propagation, and structuring in belief networks,"Artif. Intell., vol. 29, no. 3, pp. 241-288, 1986.
[20] J. Pearl,Probabilistic Reasoning in Intelligent Systems. San Mateo, CA: Morgan Kaufmann, 1988.
[21] R. D. Shachter, "Evaluating influence diagrams,"Oper. Res., vol. 34, no. 6, pp. 871-882, 1986; reprinted in [42].
[22] R. D. Shachter, and C. R. Kenley, "Gaussian influence diagrams,"Mgmt. Sci., vol. 35, pp. 527-550, 1989.
[23] G. Shafer and P. Shenoy, "Probability propagation,"Ann. Math. Artificial Intell., vol. 2, pp. 327-352, 1990.

Index Terms:
probabilistic reasoning; discrete variables; causal probabilistic networks; expert system shell; handling uncertainty by general influence networks; HUGIN; continuous variables; linear additive normally distributed variables; knowledge acquisition; belief revision; expert systems; inference mechanisms; knowledge acquisition; uncertainty handling
K.G. Olesen, "Causal Probabilistic Networks with Both Discrete and Continuous Variables," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 3, pp. 275-279, March 1993, doi:10.1109/34.204909
Usage of this product signifies your acceptance of the Terms of Use.