Robust inference of trees

Annals of Mathematics and Artificial Intelligence

Volumn 45, Issue 1-2, 2005, Pages 215-239

  Zaffalon, Marco ^a   Hutter, Marcus ^a  

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

Author keywords

Dependence; Graphical models; Imprecise Dirichlet model; Imprecise probabilities; Intervals; Mutual information; Robust inference; Spanning trees

Indexed keywords

EID: 32544450439     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10472-005-9007-9     Document Type: Article

References (29)

1. M. Abramowitz and I.A. Stegun, eds., Handbook of Mathematical Functions (Dover, 1974).
2. I.D. Aron and P. Van Hentenryck, On the complexity of the robust spanning tree problem with internal data, Operations Research Letters 32 (2004) 36-40.
3. J.-M. Bernard, 2001, Non-parametric inference about an unknown mean using the imprecise Dirichlet model, in: ISIPTA'01, eds. G. de Cooman, T. Fine and T. Seidenfeld (The Netherlands, 2001) pp. 40-50.
4. J.-M. Bernard, An introduction to the imprecise Dirichlet model for multinomial data, International Journal of Approximate 39(2-3) (2005) 123-150.
5. C.K. Chow and C.N. Liu, Approximating discrete probability distributions with dependence tress, IEEE Transactions on Information Theory, IT-14(3) (1968) 462-468.
6. N. Friedman, D. Geiger and M. Goldszmidt, Bayesian networks classifiers, Machine Learning 29(2/3) (1997) 131-163.
7. A. Gelman, J.B. Carlin, H.S. Stern and D.B. Rubin, Bayesian Data Analysis (Chapman, 1995).
8. J.B.S. Haldane, The precision of observed values of small frequencies, Biometrika 35 (1948) 297-300.
9. M. Hutter, Distribution of mutual information, in: Proceedings of NIPS*2001, eds. T.G. Dietterich, S. Vecker and Z. Ghahramani (Cambridge, MA, 2001).
10. M. Hutter, Robust estimators under the imprecise dirichlet model, in: Proc. 3rd International Symposium on Imprecise Probalities and Their Application (ISIPTA-2003), Proceedings in Informatics Vol. 18 (Canada, 2003) pp. 274-289.
11. M. Hutter and M. Zaffalon, Distribution of mutual information from complete and incomplete data, Computational Statics & Data Analysis 48(3) (2005) 633-657.
12. H. Jeffreys, An invariant form for the prior probability in estimation problems, in: Proceedings Royal Society London A, 186 (1946) pp. 453-461.
13. M.G. Kendall and A. Stuart, The Advanced Theory of Statistics, 2nd edition. (Griffin, London, 1967).
14. G.D. Kleiter, The posterior probability of Bayers nets with strong dependences, Soft Computing 3 (1999) 162-173.
15. J.B. Kruskal Jr., On the shortest spanning subtree of a graph and the traveling salesman problem, in: Proceedings of the American Mathematical Society 7 (1956) 48-50.
16. S. Kullback, Information Theory and Statistics (Dover, 1968).
17. S. Kullback and R.A. Leiber, On information and sufficiency, Annals of Mathematical Statistics 22 (1951) 79-86.
18. C. Manski, Partial Identification of Probability Distributions (Department of Economics, Northwestern University, USA: Draft book, 2002).
19. R. Montemanni, A Benders decomposition approach for the robust spanning tree problem with interval data, European Journal of Operational Research. Forthcoming.
20. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity (Prentice Hall, New York, 1982).
21. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Morgan Kaufmann, San Mateo, 1988).
22. W. Perks, Some observations on inverse probability, Journal of the Institute of Actuaries 73 (1947) 285-312.
23. M. Ramoni and P. Sebastiani, Robust learning with missing data, Machine Learning 45(2) (2001) 147-170.
24. T. Verma and J. Pearl, Equivalence and synthesis of causal models, in: UAI'90, eds. P.P. Bonissone, M. Henrion, L.N. Kanal and J.F. Lemmer (New York, 1990) pp. 220-227.
25. P. Walley, Statistical Reasoning with Imprecise Probabilities (Chapman and Hall, New York, 1991).
26. P. Walley, Inferences from multinomial data: learning about a bag of marbles, Journal of the Royal Statistical Society B 58(1) (1996) 3-57.
27. D.H. Wolpert and D.R. Wolf, Estimating functions of distributions from a finite set of samples, Physical Review E 52(6) (1995) 6841-6854.
28. H. Yaman, O.E. Karaşan and M.C. Pinar, The robust spanning tree problem with interval data, Operations Research Letters 29 (2001) 31-40.
29. M. Zaffalon, Exact credal treatment of missing data, Journal of Statistical Planning and Inference 105(1) (2002) 105-122.