Conservative inference rule for uncertain reasoning under incompleteness

Journal of Artificial Intelligence Research

Volumn 34, Issue , 2009, Pages 757-821

  Zaffalon, Marco ^a   Miranda, Enrique ^b  

^a DALLE MOLLE INSTITUTE FOR ARTIFICIAL INTELLIGENCE IDSIA   (Switzerland)

^b UNIVERSITY OF OVIEDO   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EXPERT SYSTEMS;

BAYESIAN THEORY; COHERENT LOWER PREVISIONS; GENERALISATION; INCOMPLETE INFORMATION; INFERENCE RULES; STATISTICAL INFERENCE; UNCERTAIN REASONING;

FORMAL LOGIC;

EID: 70350475361     PISSN: None     EISSN: 10769757     Source Type: Journal    
DOI: 10.1613/jair.2736     Document Type: Article

References (45)

1. Antonucci, A., & Zaffalon, M. (2006). Equivalence between Bayesian and credal nets on an updating problem. In Lawry, J., Miranda, E., Bugarin, A., Li, S., Gil, M. A., Grzegorzewski, P., & Hryniewicz, O. (Eds.), Proceedings of the third international conference on Soft Methods in Probability and Statistics, pp. 223-230, Netherlands. Springer.
2. Antonucci, A., & Zaffalon, M. (2007). Fast algorithms for robust classification with Bayesian nets. International Journal of Approximate Reasoning, 44(3) 200-223. (Pubitemid 46157171)
3. Antonucci, A., & Zaffalon, M. (2008). Decision-theoretic specification of credal networks: a unified language for uncertain modeling with sets of Bayesian networks. International Journal of Approximate Reasoning, 49(2), 345-361.
4. Antonucci, A., Zaffalon, M., Sun, Y., & de Campos, C. P. (2008). Generalized loopy 2U: a new algorithm for approximate inference in credal networks. In Jaeger, M., & Nielsen, T. D. (Eds.), Proceedings of the fourth European Workshop on Probabilistic Graphical Models, pp. 17-24.
5. Bernard, J.-M. (1996). Bayesian interpretation of frequentist procedures for a Bernoulli process. The American Statistician, 50(1), 7-13.
6. Bhaskara Rao, K. P. S., & Bhaskara Rao, M. (1983). Theory of Charges. Academic Press, London.
7. Campos, L., & Moral, S. (1995). Independence concepts for convex sets of probabilities. In Besnard, P., & Hanks, S. (Eds.), UAI-95, pp. 108-115, San Mateo. Morgan Kaufmann.
8. Corani, G., & Zaffalon, M. (2008). Learning reliable classifiers from small or incomplete data sets: the naive credal classifier 2. Journal of Machine Learning Research, 9, 581-621.
9. Couso, I., Moral, S., & Walley, P. (2000). A survey of concepts of independence for imprecise probability. Risk, Decision and Policy, 5, 165-181.
10. Cozman, F. G. (2000). Credal networks. Artificial Intelligence, 120(2), 199-233.
11. Cozman, F. G. (2005). Graphical models for imprecise probabilities. International Journal of Approximate Reasoning, 59(2-3), 167-184.
12. De Campos, C. P., & Cozman, F. G. (2005). The inferential complexity of bayesian and credal networks. In IJCAI-05, pp. 1313-1318. IJCAI.
13. De Campos, L. M., Lamata, M. T., & Moral, S. (1990). The concept of conditional fuzzy measures. International Journal of Intelligent Systems, 5, 237-246.
14. De Cooman, G., & Zaffalon, M. (2004). Updating beliefs with incomplete observations. Artificial Intelligence, 159(1-2), 75-125.
15. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, 39(1), 1-38.
16. Duda, R. O., & Hart, P. E. (1973). Pattern Classification and Scene Analysis. Wiley, New York.
17. Fagin, R., & Halpern, J. Y. (1991). A new approach to updating beliefs. In Bonissone, P. P., Henrion, M., Kanal, L. N., & Lemmer, J. F. (Eds.), Uncertainty in Artificial Intelligence, Vol. 6, pp. 347-374. North-Holland, Amsterdam.
18. Gill, R., Van der Laan, M., & Robins, J. (1997). Coarsening at random: characterisations, conjectures and counter-examples. In Lin, D.-Y. (Ed.), Proceedings of the first Seattle Conference on Biostatistics, pp. 255-294. Springer.
19. Grünwald, P., & Halpern, J. (2003). Updating probabilities. Journal of Artificial Intelligence Research, 19, 243-278. (Pubitemid 41525922)
20. Jaeger, M. (2008). Ignorability in statistical and probabilistic inference. Journal of Artificial Intelligence Research, 24, 889-917.
21. Jaffray, J.-Y. (1992). Bayesian updating and belief functions. IEEE Transactions on Systems, Man and Cybernetics, 22, 1144-1152.
22. Levi, I. (1980). The Enterprise of Knowledge. MIT Press, London.
23. Little, R. J. A., & Rubin, D. B. (1987). Statistical Analysis with Missing Data. Wiley, New York.
24. Manski, C. F. (2003). Partial Identification of Probability Distributions. Springer-Verlag, New York.
25. Miranda, E. (2008). A survey of the theory of coherent lower previsions. International Journal of Approximate Reasoning, 48(2), 628-658.
26. Miranda, E. (2009). Updating coherent previsions on finite spaces. Fuzzy Sets and Systems, 160(9), 1286-1307.
27. Miranda, E., & De Cooman, G. (2005). Coherence and independence in non-linear spaces. Tech. rep., Universidad Rey Juan Carlos, Spain. Downloadable at the address http://bellman.ciencias.uniovi.es/~emiranda/.
28. Miranda, E., & De Cooman, G. (2007). Marginal extension in the theory of coherent lower previsions. International Journal of Approximate Reasoning, 46(1), 188-225. (Pubitemid 47299294)
29. Miranda, E., & Zaffalon, M. (2009). Coherence graphs. Artificial Intelligence, 137(1), 104-144.
30. Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo.
31. Peot, M. A., & Shachter, R. D. (1998). Learning from what you don't observe. In Cooper, G. F., & Moral, S. (Eds.), Uncertainty in Artificial Intelligence (Proceedings of the Fourteenth Conference), pp. 439-446. Morgan Kaufmann Publishers, San Francisco, CA.
32. Perks, W. (1947). Some observations on inverse probability including a new indifference rule. J. Inst. Actuar., 73, 285-312.
33. Rabiner, L. (1989). A tutorial on hidden markov models and selected applications in speech recognition. Proceedings of the IEEE, 77(2), 257-286.
34. Ramoni, M., & Sebastiani, P. (2001). Robust learning with missing data. Machine Learning, 45(2), 147-170. (Pubitemid 33635983)
35. Shafer, G. (1985). Conditional probability. International Statistical Review, 53, 261-277.
36. Strassen, V. (1964). Meßfehler und Information. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 2, 273-305.
37. Troffaes, M. C. M. (2007). Decision making under uncertainty using imprecise probabilities: an introductory overview. International Journal of Approximate Reasoning, 45(1), 17-29.
38. Walley, P. (1981). Coherent lower (and upper) probabilities. Tech. rep. Statistics Research Report 22, University of Warwick, Coventry.
39. Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, New York.
40. Walley, P. (1996a). Inferences from multinomial data: learning about a bag of marbles. J. R. Statist. Soc. B, 58(1), 3-57.
41. Walley, P. (1996b). Measures of uncertainty in expert systems. Artificial Intelligence, 83(1), 1-58.
42. Walley, P., Pelessoni, R., & Vicig, P. (2004). Direct algorithms for checking consistecy and making inferences for conditional probability assessments. Journal of Statistical Planning and Inference, 126(1), 119-151. (Pubitemid 39167903)
43. Zaffalon, M. (2001). Statistical inference of the naive credal classifier. In De Cooman, G., Fine, T. L., & Seidenfeld, T. (Eds.), ISIPTA '01: Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications, pp. 384-393, The Netherlands. Shaker.
44. Zaffalon, M. (2002). Exact credal treatment of missing data. Journal of Statistical Planning and Inference, 105(1), 105-122.
45. Zaffalon, M. (2005). Conservative rules for predictive inference with incomplete data. In Cozman, F. G., Nau, R., & Seidenfeld, T. (Eds.), ISIPTA '05: Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications, pp. 406-415, Manno, Switzerland. SIPTA.