Previous |  Up |  Next


evidence theory; conditioning; independence; directed graphs
Several counterparts of Bayesian networks based on different paradigms have been proposed in evidence theory. Nevertheless, none of them is completely satisfactory. In this paper we will present a new one, based on a recently introduced concept of conditional independence. We define a conditioning rule for variables, and the relationship between conditional independence and irrelevance is studied with the aim of constructing a Bayesian-network-like model. Then, through a simple example, we will show a problem appearing in this model caused by the use of a conditioning rule. We will also show that this problem can be avoided if undirected or compositional models are used instead.
[1] Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. J. Association for Computing Machinery 30 (1983), 479-513. DOI 10.1145/2402.322389 | MR 0709830 | Zbl 0624.68087
[2] Yaghlane, B. Ben, Smets, Ph., Mellouli, K.: Belief functions independence: I. The marginal case. Internat. J. Approx. Reasoning 29 (2002), 47-70. DOI 10.1016/S0888-613X(01)00055-X | MR 1879192
[3] Yaghlane, B. Ben, Smets, Ph., Mellouli, K.: Belief functions independence: II. The conditional case. Internat. J. Approx. Reasoning 31 (2002), 31-75. DOI 10.1016/S0888-613X(02)00072-5 | MR 1940609
[4] Yaghlane, B. Ben, Smets, Ph., Mellouli, K.: Directed evidential networks with conditional belief functions. In: Proc. ECSQARU 2003 (T. D. Nielsen and N. L. Zhang, eds.), pp. 291-305. MR 2050947
[5] Benferhat, S., Dubois, D., Gracia, L., Prade, H.: Directed possibilistic graphs and possibilistic logic. In: Proc. IPMU'98 (B. Bouchon-Meunier and R. R. Yager eds.), Editions E.D.K. Paris, pp. 1470-1477.
[6] Couso, I., Moral, S., Walley, P.: Examples of independence for imprecise probabilities. In: Proc. ISIPTA'99 (G. de Cooman, F. G. Cozman, S. Moral, and P. Walley, eds.), pp. 121-130.
[7] Cozman, F. G.: Credal networks. Artificial Intelligence J. 120 (2000), 199-233. DOI 10.1016/S0004-3702(00)00029-1 | MR 1776248 | Zbl 1184.68510
[8] Daniel, M.: Belief conditioning rules for classic belief functions. In: Proc. WUPES'09 (T. Kroupa and J. Vejnarová, eds.), pp. 46-56.
[9] Cooman, G. De: Possibility theory I - III. Internat. J. General Systems 25 (1997), 291-371. DOI 10.1080/03081079708945160
[10] Guan, J. W., Bell, D. A.: Evidence Theory and its Applications. Vol. 1. North-Holland, 1991. MR 1202240
[11] Jiroušek, R., Vejnarová, J.: Compositional models and conditional independence in evidence theory. Internat. J. Approx. Reasoning 52 (2011), 316-334. DOI 10.1016/j.ijar.2010.02.005 | MR 2771963 | Zbl 1217.68214
[12] Jiroušek, R., Vejnarová, J., Daniel, M.: Compositional models for belief functions. In: Proc. ISIPTA'07 (G. De Cooman, J. Vejnarová, and M. Zaffalon, eds.) Praha, pp. 243-252.
[13] Kong, A.: Multivariate Belief Functions and Graphical Models. Doctoral disertation, Department of Statistics, Harvard University, 1986.
[14] Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton, New Jersey 1976. MR 0464340 | Zbl 0359.62002
[15] Shenoy, P. P.: Conditional independence in valuation-based systems. Internat. J. Approx. Reasoning 10 (1994), 203-234. DOI 10.1016/0888-613X(94)90001-9 | MR 1271063 | Zbl 0821.68114
[16] Studený, M.: Formal properties of conditional independence in different calculi of artificial intelligence. In: Proc. ECSQARU'93 (K. Clarke, R. Kruse, and S. Moral, eds.), Springer-Verlag, 1993, pp. 341-348.
[17] Vejnarová, J.: Conditional independence relations in possibility theory. Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems 8 (2000), 253-269. DOI 10.1142/S0218488500000186 | MR 1770487 | Zbl 1113.68536
[18] Vejnarová, J.: On conditional independence in evidence theory. In: Proc. ISIPTA'09 (T. Augustin, F. P A. Coolen, S. Moral, M. C. M. Troffaes, eds.), Durham 2009, pp. 431-440.
[19] Vejnarová, J.: An alternative approach to evidential network construction. In: Combining Soft Computing and Statistical Methods in Data Analysis (Ch. Borgelt, G. Gonzales-Rodriguez, W. Trutschnig, M. A. Lubiano, M. A. Gil, P. Grzegorzewski, and O. Hryniewicz, eds.), Oviedo 2010, pp. 619-626.
[20] Vejnarová, J.: Conditioning, conditional independence and irrelevance in evidence theory. In: Proc. ISIPTA'11 (F. Coolen, G. de Cooman, T. Fetz, and M. Oberguggenberger, eds.), Innsbruck 2011, pp. 381-390.
[21] Vejnarová, J.: Conditioning in evidence theory from the perspective of multidimensional models. In: Proc. IPMU'12 (S. Greco et al., eds.), Part III, CCIS 299, 2012, pp. 450-459. Zbl 1252.68319
[22] Vejnarová, J.: Evidential networks from a different perspective. In: Synergies of Soft Computing and Statistics for Intelligent Data Analysis, Soft Methods In Probability and Statistics, Heidelberg 2012, pp. 429-436.
[23] Vejnarová, J.: On weakness of evidential networks. In: Proc. 9th Workshop on Uncertainty Processing, pp. 190-203.
[24] Xu, H., Smets, Ph.: Evidential reasoning with conditional belief functions. In: Proc. Tenth Conference on Uncertainty in Artificial Intelligence (UAI'94), pp. 598-605.
Partner of
EuDML logo