Kybernetika 50 no. 2, 246-267, 2014

A comparison of evidential networks and compositional models

Jiřina VejnarováDOI: 10.14736/kyb-2014-2-0246

Abstract:

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.

Keywords:

conditioning, independence, evidence theory, directed graphs

Classification:

68T37

paper.pdf

References:

  1. C. Beeri, R. Fagin, D. Maier and M. Yannakakis: On the desirability of acyclic database schemes. J. Association for Computing Machinery 30 (1983), 479-513.   CrossRef
  2. B. Ben Yaghlane, Ph. Smets and K. Mellouli: Belief functions independence: I. The marginal case. Internat. J. Approx. Reasoning 29 (2002), 47-70.   CrossRef
  3. B. Ben Yaghlane, Ph. Smets and K. Mellouli: Belief functions independence: II. The conditional case. Internat. J. Approx. Reasoning 31 (2002), 31-75.   CrossRef
  4. B. Ben Yaghlane, Ph. Smets and K. Mellouli: Directed evidential networks with conditional belief functions. In: Proc. ECSQARU 2003 (T. D. Nielsen and N. L. Zhang, eds.), pp. 291-305.   CrossRef
  5. S. Benferhat, D. Dubois, L. Gracia and H. Prade: 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.   CrossRef
  6. I. Couso, S. Moral and P. Walley: 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.   CrossRef
  7. F. G. Cozman: Credal networks. Artificial Intelligence J. 120 (2000), 199-233.   CrossRef
  8. M. Daniel: Belief conditioning rules for classic belief functions. In: Proc. WUPES'09 (T. Kroupa and J. Vejnarová, eds.), pp. 46-56.   CrossRef
  9. G. De Cooman: Possibility theory I - III. Internat. J. General Systems 25 (1997), 291-371.   CrossRef
  10. J. W. Guan and D. A. Bell: Evidence Theory and its Applications. Vol. 1. North-Holland, 1991.   CrossRef
  11. R. Jiroušek and J. Vejnarová: Compositional models and conditional independence in evidence theory. Internat. J. Approx. Reasoning 52 (2011), 316-334.   CrossRef
  12. R. Jiroušek, J. Vejnarová and M. Daniel: Compositional models for belief functions. In: Proc. ISIPTA'07 (G. De Cooman, J. Vejnarová, and M. Zaffalon, eds.) Praha, pp. 243-252.   CrossRef
  13. A. Kong: Multivariate Belief Functions and Graphical Models. Doctoral disertation, Department of Statistics, Harvard University, 1986.   CrossRef
  14. G. Shafer: A Mathematical Theory of Evidence. Princeton University Press, Princeton, New Jersey 1976.   CrossRef
  15. P. P. Shenoy: Conditional independence in valuation-based systems. Internat. J. Approx. Reasoning 10 (1994), 203-234.   CrossRef
  16. M. Studený: 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.   CrossRef
  17. J. Vejnarová: Conditional independence relations in possibility theory. Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems 8 (2000), 253-269.   CrossRef
  18. J. Vejnarová: 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.   CrossRef
  19. J. Vejnarová: 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.   CrossRef
  20. J. Vejnarová: 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.   CrossRef
  21. J. Vejnarová: 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.   CrossRef
  22. J. Vejnarová: 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.   CrossRef
  23. J. Vejnarová: On weakness of evidential networks. In: Proc. 9th Workshop on Uncertainty Processing, pp. 190-203.   CrossRef
  24. H. Xu and Ph. Smets: Evidential reasoning with conditional belief functions. In: Proc. Tenth Conference on Uncertainty in Artificial Intelligence (UAI'94), pp. 598-605.   CrossRef