Summary
Support Vector Machines (SVM) is one of the most widely used technique in machines leaning. After the SVM algorithms process the data and produce some classification, it is desirable to learn how well this classification fits the data. There exist several measures of fit, among them the most widely used is kernel target alignment. These measures, however, assume that the data are known exactly. In reality, whether the data points come from measurements or from expert estimates, they are only known with uncertainty. As a result, even if we know that the classification perfectly fits the nominal data, this same classification can be a bad fit for the actual values (which are somewhat different from the nominal ones). In this paper, we show how to take this uncertainty into account when estimating the quality of the resulting classification.
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References
Cristianini, N., et al.: On kernel-target alignment. In: Dietterich, T.G., Becker, S., Ghahramani, Z. (eds.) Advances in Neural Information Processing Systems 14, MIT Press, Cambridge, Massachusetts (2002)
Ferson, S., et al.: Computing variance for interval data is NP-hard. SIGACT News 33(2), 108–118 (2002)
Garey, M.R., Johnson, D.S.: Computers and Intractability, a Guide to the Theory of NP-Completeness. WH Freeman and Company, San Francisco, California (1979)
Kreinovich, V., et al.: Computational Complexity and Feasibility of Data Processing and Interval Computations. Kluwer, Dordrecht (1997)
Kreinovich, V., et al.: Interval versions of statistical techniques, with applications to environmental analysis, bioinformatics, and privacy in statistical databases. Journal of Computational and Applied Mathematics 199, 418–423 (2007)
Jaulin, L., et al.: Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics. Springer, London (2001)
Nguyen, C.H., Ho, T.B.: Kernel matrix evaluation. In: Manuela, M., Veloso, M.M. (eds.) Proceedings of the 20th International Joint Conference on Artificial Intelligence IJCAI 2007, Hyderabad, India, January 6–12, 2007, pp. 987–992 (2007)
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover Publications, Inc., Mineola, New York (1998)
Rabinovich, S.G.: Measurement Errors and Uncertainty. Theory and Practice. Springer, Berlin (2005)
Schölkopf, B., Smola, A.J.: Learning with Kernels. MIT Press, Cambridge, Massachusetts (2002)
Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, New York (2004)
Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, New York (1995)
Wang, L., Chan, K.L.: Learning kernel parameters by using class separability measure. In: NIPS’s Sixth Kernel Machines Workshop, Whistler, Canada (2002)
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Nguyen, C.H., Ho, T.B., Kreinovich, V. (2008). Estimating Quality of Support Vector Machines Learning under Probabilistic and Interval Uncertainty: Algorithms and Computational Complexity. In: Huynh, VN., Nakamori, Y., Ono, H., Lawry, J., Kreinovich, V., Nguyen, H.T. (eds) Interval / Probabilistic Uncertainty and Non-Classical Logics. Advances in Soft Computing, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77664-2_6
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DOI: https://doi.org/10.1007/978-3-540-77664-2_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77663-5
Online ISBN: 978-3-540-77664-2
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