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76
Regularization Theory and Neural Networks Architectures
 Neural Computation
, 1995
"... We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Ba ..."
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Cited by 309 (31 self)
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We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Basis Functions approximation schemes. This paper shows that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models and some of the neural networks. In particular, we introduce new classes of smoothness functionals that lead to different classes of basis functions. Additive splines as well as some tensor product splines can be obtained from appropriate classes of smoothness functionals. Furthermore, the same generalization that extends Radial Basis Functions (RBF) to Hyper Basis Functions (HBF) also leads from additive models to ridge approximation models, containing as special cases Breiman's hinge functions, som...
In defense of onevsall classification
 Journal of Machine Learning Research
, 2004
"... Editor: John ShaweTaylor We consider the problem of multiclass classification. Our main thesis is that a simple “onevsall ” scheme is as accurate as any other approach, assuming that the underlying binary classifiers are welltuned regularized classifiers such as support vector machines. This the ..."
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Cited by 202 (0 self)
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Editor: John ShaweTaylor We consider the problem of multiclass classification. Our main thesis is that a simple “onevsall ” scheme is as accurate as any other approach, assuming that the underlying binary classifiers are welltuned regularized classifiers such as support vector machines. This thesis is interesting in that it disagrees with a large body of recent published work on multiclass classification. We support our position by means of a critical review of the existing literature, a substantial collection of carefully controlled experimental work, and theoretical arguments.
Gaussian Networks for Direct Adaptive Control
 IEEE Transactions on Neural Networks
, 1991
"... A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gaussian radial ..."
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Cited by 133 (8 self)
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A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness exhibited by the nonlinear functions, the algorithm is proven to be globally stable, with tracking errors converging to a neighborhood of zero. A constructive procedure is detailed, which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy. A stable weight adjustment mechanism is then determined using Lyapunov theory. The network construction and performance of the resulting controller are illustrated through simulations with example syst...
The neural basis of cognitive development: A constructivist manifesto
 Behavioral and Brain Sciences
, 1997
"... Quartz, S. & Sejnowski, T.J. (1997). The neural basis of cognitive development: A constructivist manifesto. ..."
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Cited by 128 (2 self)
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Quartz, S. & Sejnowski, T.J. (1997). The neural basis of cognitive development: A constructivist manifesto.
A nonparametric approach to pricing and hedging derivative securities via learning networks
 Journal of Finance
, 1994
"... http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncom ..."
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Cited by 104 (4 self)
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http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
Everything Old Is New Again: A Fresh Look at Historical Approaches
 in Machine Learning. PhD thesis, MIT
, 2002
"... 2 Everything Old Is New Again: A Fresh Look at Historical ..."
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Cited by 88 (6 self)
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2 Everything Old Is New Again: A Fresh Look at Historical
Rulebased Machine Learning Methods for Functional Prediction
 Journal of Artificial Intelligence Research
, 1995
"... We describe a machine learning method for predicting the value of a realvalued function, given the values of multiple input variables. The method induces solutions from samples in the form of ordered disjunctive normal form (DNF) decision rules. A central objective of the method and representation ..."
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Cited by 41 (3 self)
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We describe a machine learning method for predicting the value of a realvalued function, given the values of multiple input variables. The method induces solutions from samples in the form of ordered disjunctive normal form (DNF) decision rules. A central objective of the method and representation is the induction of compact, easily interpretable solutions. This rulebased decision model can be extended to search efficiently for similar cases prior to approximating function values. Experimental results on realworld data demonstrate that the new techniques are competitive with existing machine learning and statistical methods and can sometimes yield superior regression performance. 1. Introduction The problem of approximating the values of a continuous variable is described in the statistical literature as regression. Given samples of output (response) variable y and input (predictor) variables x = fx 1 :::x n g, the regression task is to find a mapping y = f(x). Relative to the spac...
Representation, Similarity, and the Chorus of Prototypes
 Minds and Machines
, 1995
"... It is proposed to conceive of representation as an emergent phenomenon that is supervenient on patterns of activity of coarsely tuned and highly redundant feature detectors. The computational underpinnings of the outlined theory of representation are (1) the properties of collections of overlappi ..."
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Cited by 41 (9 self)
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It is proposed to conceive of representation as an emergent phenomenon that is supervenient on patterns of activity of coarsely tuned and highly redundant feature detectors. The computational underpinnings of the outlined theory of representation are (1) the properties of collections of overlapping graded receptive fields, as in the biological perceptual systems that exhibit hyperacuitylevel performance, and (2) the sufficiency of a set of proximal distances between stimulus representations for the recovery of the corresponding distal contrasts between stimuli, as in multidimensional scaling. The present preliminary study appears to indicate that this concept of representation is computationally viable, and is compatible with psychological and neurobiological data. 1 Introduction A perceptual system confronted with a stimulus must (i) decide whether the stimulus belongs to an already encountered category, and (ii) if necessary, create a new category record for the stimulus a...
Approximation theory of the MLP model in neural networks
 ACTA NUMERICA
, 1999
"... In this survey we discuss various approximationtheoretic problems that arise in the multilayer feedforward perceptron (MLP) model in neural networks. Mathematically it is one of the simpler models. Nonetheless the mathematics of this model is not well understood, and many of these problems are appr ..."
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Cited by 39 (3 self)
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In this survey we discuss various approximationtheoretic problems that arise in the multilayer feedforward perceptron (MLP) model in neural networks. Mathematically it is one of the simpler models. Nonetheless the mathematics of this model is not well understood, and many of these problems are approximationtheoretic in character. Most of the research we will discuss is of very recent vintage. We will report on what has been done and on various unanswered questions. We will not be presenting practical (algorithmic) methods. We will, however, be exploring the capabilities and limitations of this model. In the first
Survey of Neural Transfer Functions
 Neural Computing Surveys
, 1999
"... The choice of transfer functions may strongly influence complexity and performance of neural networks. Although sigmoidal transfer functions are the most common there is no apriorireason why models based on such functions should always provide optimal decision borders. A large number of alternative ..."
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Cited by 35 (19 self)
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The choice of transfer functions may strongly influence complexity and performance of neural networks. Although sigmoidal transfer functions are the most common there is no apriorireason why models based on such functions should always provide optimal decision borders. A large number of alternative transfer functions has been described in the literature. A taxonomy of activation and output functions is proposed, and advantages of various nonlocal and local neural transfer functions are discussed. Several lessknown types of transfer functions and new combinations of activation/output functions are described. Universal transfer functions, parametrized to change from localized to delocalized type, are of greatest interest. Other types of neural transfer functions discussed here include functions with activations based on nonEuclidean distance measures, bicentral functions, formed from products or linear combinations of pairs of sigmoids, and extensions of such functions making rotations...