Abstract
In this chapter, we describe what are best characterized as complex adaptive systems and give several mixture of expert systems as examples of these complex systems. This background discussion is followed by three theoretical sections covering the topics of kernel-based probability estimation systems, a generalized neural network example, and a derivation of an ensemble combination and finally, a two-view ensemble combination. A summary of the equations describing the oracle follows these sections for those readers who do not want to work through all that mathematics. The next section introduces Receiver Operator Characteristic (ROC) analysis, a popular method for quantitatively assessing the performance of learning classifier systems. Next is the definition of “trouble-makers”, and how they were discovered, followed by a discussion of the development of two hybrids: an Evolutionary Programming-Adaptive boosting (EP-AB) and a Generalized Regression Neural Network (GRNN) oracle for the purpose of demonstrating the existence of the trouble-makers by using an ROC measure of performance analysis. That discussion is followed by a detailed discussion of how to perform and evaluate an ROC analysis as well as a detailed practice example for those readers not familiar with this measure of performance technology. This chapter concludes with a research study on how to use the oracle to establish if the data sample size is adequate to accurately meet a 95% confidence interval imposed on the variance (or standard deviation) for the oracle. This is an important research study as very little effort is generally put into establishing the correct data set size for accurate, predictable, and repeatable performance results.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The term nonparametric is used here to mean that the parameters of the distributions are not specified in the hypothesis. Instead, the parameters are chosen to best represent the observed data.
Abbreviations
- AB:
-
Adaptive boosting
- ANN:
-
Artificial neural network
- AUC:
-
Area under the curve
- CAS:
-
Complex Adaptive System
- EP:
-
Evolutionary programming
- FN:
-
False negative
- FP:
-
False positive
- GRNN:
-
Generalized Regression Neural Network
- LDA:
-
Linear discriminant analysis
- LR:
-
Logistic regression
- MLFN:
-
Multi-layered feed forward neural network
- MLP:
-
Multi-layer perceptron
- MOE:
-
Margin of error
- PNN:
-
Probabilistic Neural Network
- ROC:
-
Receiver operator characteristic
- SLT:
-
Statistical learning theory
- SVM:
-
Support vector machine
References
Bagnasco S, Bottigli U, Cerello P, Cheran S, Delogu P, Fantacci ME, Fauci F, Forni G, Lauria A, Torres EL, Magro R, Masala GL, Oliva P, Palmiero R, Ramello L, Raso G, Retico A, Sitta M, Stumbo S, Tangaro S, Zanon E (2005) GPCALMA: a GRID based tool for mammographic screening. Methods Inf Med 44(2):244–248
Baker JA, Kornguth PJ, Lo JY, Williford ME, Floyd CE Jr (1995) Breast cancer: prediction with artificial neural network based on BI-RADS standardized lexicon. Radiology 196:817–822
BI-RADS (1993) Breast Imaging—Reporting and Data System (BI-RADS). American College of Radiology, Virginia
Brown G, Wyatt J, Harris R, Yao X (2005) Diversity creation methods: a survey and categorisation. Inf Fusion 6:5–20
Cacoullos T (1966) Estimation of a multivariate density. Ann Inst Stat Math 18:179–189
Hand DJ, Till RJ (2001) A simple generalisation of the area under the ROC curve for multiple class classification problems. Mach Learn 45(2):171–186
Land WH, Masters T, Lo JY (2000a) Performance evaluation using the GRNN Oracle and a new evolutionary programming/adaptive boosting hybrid for breast cancer benign/malignant diagnostic aids, ANNIE
Land WH, Masters T, Lo JY (2000b) Application of a new evolutionary programming/adaptive boosting hybrid to breast cancer diagnosis. In: IEEE congress on evolutionary computation proceedings (CEC2000)
Land WH, Masters TD, Lo JY (2000c) Application of a GRNN oracle to the intelligent combination of several breast cancer benign/malignant predictive paradigms. In: Hanson KM (ed) Medical imaging 2000; image processing, proceedings of SPIE, San Diego, CA, pp 77–85
Land WH, Masters T, Lo JY, McKee D, (2000d) Using evolutionary computation to develop neural network breast cancer benign/malignant classification models. In: 4th world conference on systemics, cybernetics and informatics (SCI2000), vol 10, pp 343–347
Land WH, Margolis D, Kallergi M, Heine JJ (2010) A kernel approach for ensemble decision combinations with two-view mammography applications. Int J Funct Inf Pers Med 3(2):157–182
Lo JY, Baker JA, Kornguth PJ, Floyd CE Jr (1995) Computer-aided diagnosis of breast cancer: artificial neural network approach for optimized merging of mammographic features. Acad Radiol 2:841–850
Lo JY, Baker JA, Kornguth PJ, Iglehart JD, Floyd CE Jr (1999) Effect of patient history data on the prediction of breast cancer from mammographic findings with artificial neural networks. Acad Radiol 6:10–15
Masters T (1995) Advanced algorithms for neural networks, A C++ source book. Wiley, New York, ISBN 0-471-10588-09 (paper/disk)
Masters T, Land WH (1997) A new training method for the general regression neural network. In: IEEE international SMC conference proceedings, pp 1990–1995
Masters T, Land WH, Maniccam S (1998) An oracle based on the general regression neural network. In: IEEE international conference on systems, man, and cybernetics—SMC, vol 2, pp 1615–1618
Mercer J (1909) Functions of positive and negative type, and their connection with the theory of integral equations. Philos Trans R Soc Lond A 209:415–446
Nadaraya EA (1964) On estimating regression. Theory Probab Appl 9:141–142
Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33(3):1065
Pierson M (2002) Complex adaptive systems, a definition. http://radio-weblogs.com/0107584/stories/2002/05/13/complexAdaptiveSystemsADefinition.html [last visited 2015-05-19]
Polikar R (2006) Ensemble based systems in decision making. IEEE Circuits Syst Mag 6(3):21–45
Powers DMW (2011) Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation. J Mach Learn Technol 2(1):37–63
Raponi M, Zhang Y, Yu J, Chen G, Lee G, Taylor JMG, Macdonald J, Thomas D, Moskaluk C, Wang Y, Beer DG (2006) Gene expression signatures for predicting prognosis of squamous cell and adenocarcinomas of the lung. Cancer Res 66(15):7466–7472. [http://cancerres.aacrjournals.org/cgi/content/abstract/66/15/7466]
Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. Cambridge University Press, Cambridge
Shedden K, Taylor JMG, Enkemann SA, Tsao M-S, Yeatman TJ, Gerald WL, Eschrich S, Jurisica I, Giordano TJ, Misek DE, Chang AC, Zhu CQ, Strumpf D, Hanash S, Shepherd FA, Ding K, Seymour L, Naoki K, Pennell N, Weir B, Verhaak R, Ladd-Acosta C, Golub T, Gruidl M, Sharma A, Szoke J, Zakowski M, Rusch V, Kris M, Viale A, Motoi N, Travis W, Conley B, Seshan VE, Meyerson M, Kuick R, Dobbin KK, Lively T, Jacobson JW (2008) Beer, gene expression–based survival prediction in lung adenocarcinoma: a multi-site, blinded validation study. Nat Med 14(8):822–827
Specht DF (1990) Probabilistic neural networks. Neural Netw 3:109–118
Specht DF (1991) A general regression neural network. IEEE Trans Neural Netw 2:568–576
Stern H (2003) Improving on the mixture of experts algorithm. Computational Neuroscience Project, Dalhousie University, Halifax
Tang K, Wang R, Chen T (2011), Towards maximizing the area under the ROC for Multi_class classification problems. In: Proceedings 25th conference on AI, AAAI, pp 483–488
Taylor JR (1982) An introduction to error analysis. University Science Books, Mill Valley
Vapnik VN (1998) Statistical learning theory. Wiley, New York
Vapnik VN (2000) The nature of statistical learning theory. Springer, New York
Watson GS (1964) Smooth regression analysis. Sankhya 26:359–372
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Land, W.H., Schaffer, J.D. (2020). The Generalized Regression Neural Network Oracle. In: The Art and Science of Machine Intelligence. Springer, Cham. https://doi.org/10.1007/978-3-030-18496-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-18496-4_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-18495-7
Online ISBN: 978-3-030-18496-4
eBook Packages: EngineeringEngineering (R0)