×
Monney, Paul-André; Chan, Moses; Romberg, Paul

A belief function classifier based on information provided by noisy and dependent features. (English) Zbl 1217.68215

Int. J. Approx. Reasoning 52, No. 3, 335-352 (2011).
Summary: A model and method are proposed for dealing with noisy and dependent features in classification problems. The knowledge base consists of uncertain logical rules forming a probabilistic argumentation system. Assumption-based reasoning is the inference mechanism that is used to derive information about the correct class of the object. Given a hypothesis regarding the correct class, the system provides a symbolic expression of the arguments for that hypothesis as a logical disjunctive normal form. These arguments turn into degrees of support for the hypothesis when numerical weights are assigned to them, thereby creating a support function on the set of possible classes. Since a support function is a belief function, the pignistic transformation is then applied to the support function and the object is placed into the class with maximal pignistic probability.

Cited in 2 Documents

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence

Keywords:

Dempster-Shafer theory; evidence theory; object classification; noisy measurements; dependent features

Software:

ABEL
PDF BibTeX XML Cite
\textit{P.-A. Monney} et al., Int. J. Approx. Reasoning 52, No. 3, 335--352 (2011; Zbl 1217.68215)
Full Text: DOI

References:

[1] Denoeux, T., A k-nearest neighbor classification rule based on Dempster-Shafer theory, IEEE Transactions on Systems, Man and Cybernetics, 25, 05, 804-813 (1995)
[2] Denoeux, T., A neural network classifier based on Dempster-Shafer theory, IEEE Transactions on Systems, Man and Cybernetics A, 30, 2, 131-150 (2000)
[3] Denoeux, T.; Zouhal, L. M., Handling possibilistic labels in pattern classification using evidential reasoning, Fuzzy Sets and Systems, 122, 3, 47-62 (2001) · Zbl 1063.68635
[4] Denoeux, T.; Smets, P., Classification using belief functions: the relationship between the case-based and model-based approaches, IEEE Transactions on Systems, Man and Cybernetics B, 36, 6 (2006)
[5] Quost, B.; Denoeux, T.; Masson, M.-H., Pairwise classifier combination using belief functions, Pattern Recognition Letters, 28, 5, 644-653 (2007)
[6] Friedman, N.; Geiger, D.; Goldszmidt, M., Bayesian network classifiers, Machine Learning, 29, 2-3, 131-163 (1997) · Zbl 0892.68077
[8] Smets, P., Decision making in the TBM: the necessity of the pignistic transformation, International Journal of Approximate Reasoning, 38, 133-147 (2005) · Zbl 1065.68098
[9] Shafer, G., A Mathematical Theory of Evidence (1976), Princeton University Press · Zbl 0359.62002
[10] Kohlas, J.; Monney, P. A., A Mathematical Theory of Hints, Lecture Notes in Economics and Mathematical Systems, vol. 425 (1995), Springer: Springer Berlin · Zbl 0833.62005
[11] Smets, P.; Kennes, R., The transferable belief model, Artificial Intelligence, 66, 191-243 (1994) · Zbl 0807.68087
[12] Smets, P., Practical uses of belief functions, (Laskey, K. B.; Prade, H., Uncertainty in Artificial Intelligence, vol. 15 (1999), Stockholm: Stockholm Sweden)
[13] Smets, P., Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem, International Journal of Approximate Reasoning, 9, 1-35 (1993) · Zbl 0796.68177
[14] Smets, P., The transferable model for quantified belief representation, (Smets, P., Quantified Representation of Uncertainty and Imprecision. Quantified Representation of Uncertainty and Imprecision, Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 1 (1998), Kluwer: Kluwer Dordrech), 267-301 · Zbl 0939.68112
[15] Dempster, A. P., A generalization of Bayesian inference, Journal of the Royal Statistical Society Series B, 30, 205-247 (1968) · Zbl 0169.21301
[16] Aregui, A.; Denoeux, T., Constructing consonant belief functions from sample data using confidence sets of pignistic probabilities, International Journal of Approximate Reasoning, 49, 3, 575-594 (2008) · Zbl 1184.68499
[17] Haenni, R.; Kohlas, J.; Lehmann, N., Probabilistic argumentation systems, (Kohlas, J.; Moral, S., Algorithms for Uncertainty and Defeasible Reasoning. Algorithms for Uncertainty and Defeasible Reasoning, Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 5 (2000), Kluwer: Kluwer Dordrecht) · Zbl 0987.68076
[18] Kohlas, J.; Haenni, R., Propositional information systems, Journal of Logic and Computation, 9, 5, 651-681 (1999) · Zbl 0941.03030
[20] Haenni, R., Probabilistic argumentation, Journal of Applied Logic, 7, 2, 155-176 (2009) · Zbl 1183.68617
[21] Laskey, K. B.; Lehner, P. E., Assumptions beliefs and probabilities, Artificial Intelligence, 41, 65-77 (1989)
[22] Pearl, J., Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (1988), Morgan Kaufman
[23] Kohlas, J., Information Algebras. Generic Structures for Inference. Discrete Mathematics and Theoretical Computer Science (2003), Springer: Springer London
[25] Monney, P. A., A Mathematical Theory of Arguments for Statistical Evidence. Contributions to Statistics (2003), Physica Verlag (Springer)
[26] Kohlas, J., Uncertain information: random variables in graded semilattices, International Journal of Approximate Reasoning, 46, 1, 17-34 (2007) · Zbl 1151.68050
[27] Kohlas, J.; Monney, P. A., An algebraic theory for statistical information based on the theory of hints, International Journal of Approximate Reasoning, 48, 2, 378-398 (2008) · Zbl 1239.62008
[29] Monney, P. A.; Bertschy, R., A generalization of the algorithm of Heidtmann to non-monotone formulas, Journal of Computational and Applied Mathematics, 76, 55-76 (1996) · Zbl 0868.68102
[30] Monney, P. A.; Chan, M., Modeling dependence in Dempster-Shafer theory, International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 15, 1, 93-113 (2007) · Zbl 1115.68149
[31] Fisher, R. A., The fiducial argument in statistical inference, Annals of Eugenics, 9, 391-398 (1935)
[32] David, A. P.; Stone, M., The functional-model basis of fiducial inference, The Annals of Statistics, 10, 4, 1054-1067 (1982) · Zbl 0511.62010
[34] Silverman, B., Density Estimation for Statistics and Data Analysis (1986), Chapman & Hall: Chapman & Hall London · Zbl 0617.62042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.