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Erschienen in:
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2016 | OriginalPaper | Buchkapitel

Nonparametric Estimation of Edge Values of Regression Functions

verfasst von : Tomasz Galkowski, Miroslaw Pawlak

Erschienen in: Artificial Intelligence and Soft Computing

Verlag: Springer International Publishing

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Abstract

In this article we investigate the problem of regression functions estimation in the edges points of their domain. We refer to the model \(y_i = R\left( {x_i } \right) + \epsilon _i ,\,i = 1,2, \ldots n\), where \(x_i\) is assumed to be the set of deterministic inputs, \(x_i \in D\), \(y_i\) is the set of probabilistic outputs, and \(\epsilon _i\) is a measurement noise with zero mean and bounded variance. R(.) is a completely unknown function. The possible solution of finding unknown function is to apply the algorithms based on the Parzen kernel [13, 31]. The commonly known drawback of these algorithms is that the error of estimation dramatically increases if the point of estimation x is drifting to the left or right bound of interval D. This fact makes it impossible to estimate functions exactly in edge values of domain.
The main goal of this paper is an application of NMS algorithm (introduced in [11]), basing on integral version of the Parzen method of function estimation by combining the linear approximation idea. The results of numerical experiments are presented.

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Vorheriges Kapitel On the Cesàro-Means-Based Orthogonal Series Approach to Learning Time-Varying Regression Functions
Nächstes Kapitel Hybrid Splitting Criterion in Decision Trees for Data Stream Mining
Literatur
1.
Aghdam, M.H., Heidari, S.: Feature selection using particle swarm optimization in text categorization. J. Artif. Intell. Soft Comput. Res. 5(4), 231–238 (2015)CrossRef
2.
Bas, E.: The Training of multiplicative neuron model artificial neural networks with differential evolution algorithm for forecasting. J. Artif. Intell. Soft Comput. Res. 6(1), 5–11 (2016)CrossRef
3.
Bertini Jr., J.R., Carmo, N.M.: Enhancing constructive neural network performance using functionally expanded input data. J. Artif. Intell. Soft Comput. Res. 6(2), 119–131 (2016)
4.
Chen, S.X.: Beta kernel estimators for density functions. J. Stat. Plann. Infer. 139, 2269–2283 (2009)CrossRef
5.
Chu, J.L., Krzyzak, A.: The recognition of partially occluded objects with support vector machines, convolutional neural networks and deep belief networks. J. Artif. Intell. Soft Comput. Res. 4(1), 5–19 (2014)CrossRef
6.
Cierniak, R., Rutkowski, L.: On image compression by competitive neural networks and optimal linear predictors. Sig. Process.-Image Commun. 15(6), 559–565 (2000)CrossRef
7.
Duch, W., Korbicz, J., Rutkowski, L., Tadeusiewicz, R. (eds.): Biocybernetics and Biomedical Engineering 2000. Neural Networks, vol. 6. Akademicka Oficyna Wydawnicza, EXIT, Warsaw (2000) (in Polish)
8.
Galkowski, T., Rutkowski, L.: Nonparametric recovery of multivariate functions with applications to system identification. In: Proceedings of the IEEE, vol. 73, pp. 942–943, New York (1985)
9.
Galkowski, T., Rutkowski, L.: Nonparametric fitting of multivariable functions. IEEE Trans. Autom. Control AC–31, 785–787 (1986)CrossRefMATH
10.
Galkowski, T.: Nonparametric estimation of boundary values of functions. Arch. Control Sci. 3(1–2), 85–93 (1994)MathSciNetMATH
11.
Gałkowski, T.: Kernel estimation of regression functions in the boundary regions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS, vol. 7895, pp. 158–166. Springer, Heidelberg (2013)CrossRef
12.
Galkowski, T., Pawlak, M.: Nonparametric extension of regression functions outside domain. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS, vol. 8467, pp. 518–530. Springer, Heidelberg (2014)CrossRef
13.
Gasser, T., Muller, H.G.: Kernel estimation of regression functions. Lecture Notes in Mathematics, vol. 757. Springer, Heidelberg (1979)MATH
14.
Greblicki, W., Rutkowski, L.: Density-free bayes risk consistency of nonparametric pattern recognition procedures. Proc. IEEE 69(4), 482–483 (1981)CrossRef
15.
Greblicki, W., Rutkowska, D., Rutkowski, L.: An orthogonal series estimate of time-varying regression. Ann. Inst. Stat. Math. 35(1), 215–228 (1983)MathSciNetCrossRefMATH
16.
Hazelton, M.L., Marshall, J.C.: Linear boundary kernels for bivariate density estimation. Stat. Prob. Lett. 79, 999–1003 (2009)MathSciNetCrossRefMATH
17.
18.
Karunamuni, R.J., Alberts, T.: A locally adaptive transformation method of boundary correction in kernel density estimation. J. Stat. Plann. Infer. 136, 2936–2960 (2006)MathSciNetCrossRefMATH
19.
Kitajima, R., Kamimura, R.: Accumulative information enhancement in the self-organizing maps and its application to the analysis of mission statements. J. Artif. Intell. Soft Comput. Res. 5(3), 161–176 (2015)CrossRef
20.
Knop, M., Kapuscinski, T., Mleczko, W.K.: Video key frame detection based on the restricted Boltzmann machine. J. Appl. Math. Comput. Mech. 14(3), 49–58 (2015)CrossRef
21.
Korytkowski, M., Nowicki, R., Scherer, R.: Neuro-fuzzy rough classifier ensemble. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds.) ICANN 2009, Part I. LNCS, vol. 5768, pp. 817–823. Springer, Heidelberg (2009)CrossRef
22.
Korytkowski, M., Rutkowski, L., Scherer, R.: Fast image classification by boosting fuzzy classifiers. Inf. Sci. 327, 175–182 (2016)MathSciNetCrossRef
23.
Koshiyama, A.S., Vellasco, M., Tanscheit, R.: GPFIS-control: a genetic fuzzy system for control tasks. J. Artif. Intell. Soft Comput. Res. 4(3), 167–179 (2014)CrossRef
24.
Kyung-Joon, C., Schucany, W.R.: Nonparametric kernel regression estimation near endpoints. J. Stat. Plann. Inf. 66, 289–304 (1998)MathSciNetCrossRefMATH
25.
Marshall, J.C., Hazelton, M.L.: Boundary kernels for adaptive density estimators on regions with irregular boundaries. J. Multivar. Anal. 101, 949–963 (2010)MathSciNetCrossRefMATH
26.
Laskowski, L.: A novel hybrid-maximum neural network in stereo-matching process. Neural Comput. Appl. 23(7–8), 2435–2450 (2013)CrossRef
27.
Laskowski, L., Jelonkiewicz, J.: Self-correcting neural network for stereo-matching problem solving. Fundamenta Informaticae 138, 1–26 (2015)MathSciNetCrossRefMATH
28.
29.
Nikulin, V.: Prediction of the shoppers loyalty with aggregated data streams. J. Artif. Intell. Soft Comput. Res. 6(2), 69–79 (2016)MathSciNetCrossRef
30.
Nowak, B.A., Nowicki, R.K., Starczewski, J.T., Marvuglia, A.: The learning of neuro-fuzzy classifier with fuzzy rough sets for imprecise datasets. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS, vol. 8467, pp. 256–266. Springer, Heidelberg (2014)CrossRef
31.
32.
Poměnková-Dluhá, J.: Edge Effects of Gasser-Müller Estimator, Mathematica 15, Brno, Masaryk University, pp. 307–314 (2004)
33.
Rafajlowicz, E.: Nonparametric least squares estimation of a regression function statistics. J. Theor. Appl. Stat. 19(3), 349–358 (1988)MathSciNetMATH
34.
Rafajlowicz, E., Schwabe, R.: Halton and hammersley sequences in multivariate nonparametric regression. Stat. Prob. Lett. 76(8), 803–812. Elsevier (2006)
35.
Rutkowska, A.: Influence of membership function’s shape on portfolio optimization results. J. Artif. Intell. Soft Comput. Res. 6(1), 45–54 (2016)CrossRef
36.
Rutkowski, L.: Sequential estimates of probability densities by orthogonal series and their application in pattern classification. IEEE Trans. Syst. Man Cybern. SMC–10(12), 918–920 (1980)MathSciNetMATH
37.
Rutkowski, L.: On bayes risk consistent pattern recognition procedures in a quasi-stationary environment. IEEE Trans. Pattern Anal. Mach. Intell. PAMI–4(1), 84–87 (1982)MathSciNetCrossRefMATH
38.
Rutkowski, L.: Online identification of time-varying systems by nonparametric techniques. IEEE Trans. Autom. Control 27(1), 228–230 (1982)MathSciNetCrossRefMATH
39.
Rutkowski, L.: On nonparametric identification with prediction of time-varying systems. IEEE Trans. Autom. Control AC–29, 58–60 (1984)CrossRefMATH
40.
Rutkowski, L.: Nonparametric identification of quasi-stationary systems. Syst. Control Lett. 6, 33–35. Amsterdam (1985)
41.
Rutkowski, L.: Real-time identification of time-varying systems by non-parametric algorithms based on parzen kernels. Int. J. Syst. Sci. 16, 1123–1130 (1985)CrossRefMATH
42.
Rutkowski, L.: A general approach for nonparametric fitting of functions and their derivatives with applications to linear circuits identification. IEEE Trans. Circuits Syst. 33, 812–818 (1986)CrossRefMATH
43.
Rutkowski, L.: Sequential pattern recognition procedures derived from multiple Fourier series. Pattern Recogn. Lett. 8, 213–216 (1988)CrossRefMATH
44.
Rutkowski, L.: Application of multiple fourier series to identification of multivariable nonstationary systems. Int. J. Syst. Sci. 20(10), 1993–2002 (1989)MathSciNetCrossRefMATH
45.
Rutkowski, L.: Non-parametric learning algorithms in the time-varying environments. Sig. Process. 18(2), 129–137 (1989)MathSciNetCrossRef
46.
Rutkowski, L., Rafajłowicz, E.: On global rate of convergence of some nonparametric identification procedures. IEEE Trans. Autom. Control AC–34(10), 1089–1091 (1989)MathSciNetCrossRefMATH
47.
Rutkowski, L.: Identification of MISO nonlinear regressions in the presence of a wide class of disturbances. IEEE Trans. Inf. Theory IT–37, 214–216 (1991)MathSciNetCrossRefMATH
48.
Rutkowski, L.: Multiple fourier series procedures for extraction of nonlinear regressions from noisy data. IEEE Trans. Sig. Process. 41(10), 3062–3065 (1993)CrossRefMATH
49.
Rutkowski, L.: Generalized regression neural networks in time-varying environment. IEEE Trans. Neural Netw. 15(3), 576–596 (2004)CrossRef
50.
Rutkowski, L.: Adaptive probabilistic neural networks for pattern classification in time-varying environment. IEEE Trans. Neural Netw. 15(4), 811–827 (2004)MathSciNetCrossRef
51.
Rutkowski, L., Pietruczuk, L., Duda, P., Jaworski, M.: Decision trees for mining data streams based on the mcdiarmid’s bound. IEEE Trans. Knowl. Data Eng. 25(6), 1272–1279 (2013)CrossRef
52.
Rutkowski, L., Jaworski, M., Duda, P., Pietruczuk, L.: Decision trees for mining data streams based on the gaussian approximation. IEEE Trans. Knowl. Data Eng. 26(1), 108–119 (2014)CrossRef
53.
Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: The CART decision trees mining data streams. Inf. Sci. 266, 1–15 (2014)CrossRef
54.
Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: A new method for data stream mining based on the misclassification error. IEEE Trans. Neural Netw. Learn. Syst. 26(5), 1048–1059 (2015)MathSciNetCrossRef
55.
Schuster, E.F.: Incorporating support constraints into nonparametric estimators of densities. Commun. Stat. Part A - Theory Methods 14, 1123–1136 (1985)MathSciNetCrossRefMATH
56.
Skubalska-Rafajlowicz, E.: Pattern recognition algorithms based on space-filling curves and orthogonal expansions. IEEE Trans. Inf. Theory 47(5), 1915–1927 (2001)MathSciNetCrossRefMATH
57.
Skubalska-Rafajlowicz, E.: Random projection RBF nets for multidimensional density estimation. Int. J. Appl. Math. Comput. Sci. 18(4), 455–464 (2008)MathSciNetCrossRefMATH
58.
Szarek, A., Korytkowski, M., Rutkowski, L., Scherer, R., Szyprowski, J.: Application of neural networks in assessing changes around implant after total hip arthroplasty. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS, vol. 7268, pp. 335–340. Springer, Heidelberg (2012)CrossRef
59.
Wang, Z., Zhang-Westmant, L.: New ranking method for fuzzy numbers by their expansion center. J. Artif. Intell. Soft Comput. Res. 4(3), 181–187 (2014)CrossRef
60.
61.
Zhang, S., Karunamuni, R.J.: Deconvolution boundary kernel method in nonparametric density estimation. J. Stat. Plann. Inf. 139, 2269–2283 (2009)MathSciNetCrossRefMATH
62.
Metadaten
Titel
Nonparametric Estimation of Edge Values of Regression Functions
verfasst von
Tomasz Galkowski
Miroslaw Pawlak
Copyright-Jahr
2016
Buch
Artificial Intelligence and Soft Computing

Print ISBN: 978-3-319-39383-4

Electronic ISBN: 978-3-319-39384-1

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-39384-1_5