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Support vector interval regression networks for interval regression analysis. (English) Zbl 1043.62064
Summary: In this paper, support vector interval regression networks (SVIRNs) are proposed for interval regression analysis. The SVIRNs consist of two radial basis function networks. One network identifies the upper side of data interval, and the other network identifies the lower side of the data intervals. Because the support vector regression (SVR) approach is equivalent to solving a linear constrained quadratic programming problem, the number of hidden nodes and the initial values of adjustable parameters can be easily obtained. Since the selection of a parameter \(\varepsilon\) in the SVR approach may seriously affect the modeling performance, a two-step approach is proposed to properly select the \(\varepsilon\) value. After the SVR approach with the selected \(\varepsilon\), an initial structure of SVIRNs can be obtained.
Besides, outliers will not significantly affect the upper and lower bound interval obtained through the proposed two-step approach. Consequently, a traditional back-propagation (BP) learning algorithm can be used to adjust the initial structure networks of SVIRNs under training data sets without or with outliers. Due to the better initial structure of SVIRNs obtained by the SVR approach, the convergence rate of SVIRNs is faster than the conventional networks with BP learning algorithms or with robust BP learning algorithms for interval regression analysis. Four examples are provided to show the validity and applicability of the proposed SVIRNs.

62J99 Linear inference, regression
62M45 Neural nets and related approaches to inference from stochastic processes
65C60 Computational problems in statistics (MSC2010)
90C90 Applications of mathematical programming
Full Text: DOI
[1] Chen, D.S.; Jain, R.C., A robust back-propagation learning algorithm for function approximation, IEEE trans. neural networks, 5, 467-478, (1994)
[2] Cheng, C.B.; Lee, E.S., Fuzzy regression with radial basis function network, Fuzzy sets and systems, 119, 291-301, (2001)
[3] Chuang, C.C.; Su, S.F.; Hsiao, C.C., The annealing robust back-propagation (ARBP) learning algorithm, IEEE trans. neural networks, 11, 1067-1077, (2000)
[4] Cichocki, A.; Unbehauen, R., Neural networks for optimization and signal processing, (1993), Wiley New York · Zbl 0824.68101
[5] Drucker, H., Support vector regression machines, Neural information processing systems, Vol. 9, (1997), MIT Press Cambridge, MA
[6] Evans, M.; Hastings, N.; Peacock, B., Statistical distributions, (1993), Wiley New York
[7] Freund, J.E.; Williams, F.J., Dictionary/outline of basic statistics, (1966), Dover New York · Zbl 0192.26303
[8] T. Hashiyama, T. Furuhash, Y. Uchikawa, An interval fuzzy model using a fuzzy neural network, Proc. Internat. Joint Conf. Neural Networks, Baltimore, MD, 1992, pp. 745-750.
[9] Heshmaty, B.; Kandel, A., Fuzzy linear regression and its applications to forecasting in uncertain environment, Fuzzy sets and systems, 15, 159-191, (1985) · Zbl 0566.62099
[10] Huang, L.; Zhang, B.L.; Huang, Q., Robust interval regression analysis using neural networks, Fuzzy sets and systems, 97, 337-347, (1998)
[11] Huber, P.J., Robust statistics, (1981), Wiley New York · Zbl 0536.62025
[12] Ishibuchi, H.; Nii, M., Fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks, Fuzzy sets and systems, 119, 200-273, (2001) · Zbl 0964.62051
[13] H. Ishibuchi, H. Tanaka, Several formulations of interval regression analysis, Proc. Sino-Japan Joint Meeting on Fuzzy Sets and Systems, Beijing, China, 1990, pp. B2-2.
[14] Ishibuchi, H.; Tanaka, H., Fuzzy regression analysis using neural networks, Fuzzy sets and systems, 50, 57-65, (1992)
[15] Ishibuchi, H.; Tanaka, H.; Okada, H., An architecture of neural networks with interval weights and its application to fuzzy regression analysis, Fuzzy sets and systems, 57, 27-39, (1993) · Zbl 0790.62072
[16] M. Kaneyoshi, H. Tanaka, M. Kamei, H. Farata, New system identification technique using fuzzy regression analysis, Proc. 1st Internat. Symp. on Uncertainty Modeling and Analysis, Maryland, MD, 1990, pp. 528-533.
[17] Peters, G., Fuzzy linear regression with fuzzy intervals, Fuzzy sets and systems, 63, 45-54, (1994)
[18] Rousseeuw, P.J.; Leroy, M.A., Robust regression and outlier detection, (1987), Wiley New York
[19] Schölkopf, B., Comparing support vector machines with Gaussian kernels to radial basis function classifiers, IEEE trans. signal process., 45, 2758-2765, (1997)
[20] A.J. Smola, B. Schölkopf, A tutorial on support vector regression, Neuro COLT Technical Report TR-1998-030, Royal Holloway College.
[21] Vapnik, V., The nature of statistical learning theory, (1995), Springer Berlin · Zbl 0833.62008
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