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773
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 587 (12 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additive expansions based on any tting criterion. Specic algorithms are presented for least{squares, least{absolute{deviation, and Huber{M loss functions for regression, and multi{class logistic likelihood for classication. Special enhancements are derived for the particular case where the individual additive components are regression trees, and tools for interpreting such \TreeBoost" models are presented. Gradient boosting of regression trees produces competitive, highly robust, interpretable procedures for both regression and classication, especially appropriate for mining less than clean data. Connections between this approach and the boosting methods of Freund and Shapire 1996, and Frie...
Protein Secondary Structure Prediction . . .
 JO MOL B/O/. (1999) 292, 195202 .GG
, 1999
"... ..."
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 317 (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...
Residual Algorithms: Reinforcement Learning with Function Approximation
 In Proceedings of the Twelfth International Conference on Machine Learning
, 1995
"... A number of reinforcement learning algorithms have been developed that are guaranteed to converge to the optimal solution when used with lookup tables. It is shown, however, that these algorithms can easily become unstable when implemented directly with a general functionapproximation system, such ..."
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Cited by 243 (5 self)
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A number of reinforcement learning algorithms have been developed that are guaranteed to converge to the optimal solution when used with lookup tables. It is shown, however, that these algorithms can easily become unstable when implemented directly with a general functionapproximation system, such as a sigmoidal multilayer perceptron, a radialbasisfunction system, a memorybased learning system, or even a linear functionapproximation system. A new class of algorithms, residual gradient algorithms, is proposed, which perform gradient descent on the mean squared Bellman residual, guaranteeing convergence. It is shown, however, that they may learn very slowly in some cases. A larger class of algorithms, residual algorithms, is proposed that has the guaranteed convergence of the residual gradient algorithms, yet can retain the fast learning speed of direct algorithms. In fact, both direct and residual gradient algorithms are shown to be special cases of residual algorithms, and it is s...
Optimal Unsupervised Learning in a SingleLayer Linear Feedforward Neural Network
, 1989
"... A new approach to unsupervised learning in a singlelayer linear feedforward neural network is discussed. An optimality principle is proposed which is based upon preserving maximal information in the output units. An algorithm for unsupervised learning based upon a Hebbian learning rule, which achie ..."
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Cited by 223 (0 self)
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A new approach to unsupervised learning in a singlelayer linear feedforward neural network is discussed. An optimality principle is proposed which is based upon preserving maximal information in the output units. An algorithm for unsupervised learning based upon a Hebbian learning rule, which achieves the desired optimality is presented, The algorithm finds the eigenvectors of the input correlation matrix, and it is proven to converge with probability one. An implementation which can train neural networks using only local "synaptic" modification rules is described. It is shown that the algorithm is closely related to algorithms in statistics (Factor Analysis and Principal Components Analysis) and neural networks (Selfsupervised Backpropagation, or the "encoder" problem). It thus provides an explanation of certain neural network behavior in terms of classical statistical techniques. Examples of the use of a linear network for solving image coding and texture segmentation problems are presented. Also, it is shown that the algorithm can be used to find "visual receptive fields" which are qualitatively similar to those found in primate retina and visual cortex.
A Theory of Networks for Approximation and Learning
 Laboratory, Massachusetts Institute of Technology
, 1989
"... Learning an inputoutput mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multidimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, t ..."
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Cited by 200 (24 self)
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Learning an inputoutput mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multidimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, this form of learning is closely related to classical approximation techniques, such as generalized splines and regularization theory. This paper considers the problems of an exact representation and, in more detail, of the approximation of linear and nonlinear mappings in terms of simpler functions of fewer variables. Kolmogorov's theorem concerning the representation of functions of several variables in terms of functions of one variable turns out to be almost irrelevant in the context of networks for learning. Wedevelop a theoretical framework for approximation based on regularization techniques that leads to a class of threelayer networks that we call Generalized Radial Basis Functions (GRBF), since they are mathematically related to the wellknown Radial Basis Functions, mainly used for strict interpolation tasks. GRBF networks are not only equivalent to generalized splines, but are also closely related to pattern recognition methods suchasParzen windows and potential functions and to several neural network algorithms, suchas Kanerva's associative memory,backpropagation and Kohonen's topology preserving map. They also haveaninteresting interpretation in terms of prototypes that are synthesized and optimally combined during the learning stage. The paper introduces several extensions and applications of the technique and discusses intriguing analogies with neurobiological data.
Deep Dyslexia: A Case Study of Connectionist Neuropsychology
, 1993
"... Deep dyslexia is an acquired reading disorder marked by the occurrence of semantic errors (e.g., reading RIVER as "ocean"). In addition, patients exhibit a number of other symptoms, including visual and morphological effects in their errors, a partofspeech effect, and an advantage for co ..."
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Cited by 143 (27 self)
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Deep dyslexia is an acquired reading disorder marked by the occurrence of semantic errors (e.g., reading RIVER as "ocean"). In addition, patients exhibit a number of other symptoms, including visual and morphological effects in their errors, a partofspeech effect, and an advantage for concrete over abstract words. Deep dyslexia poses a distinct challenge for cognitive neuropsychology because there is little understanding of why such a variety of symptoms should cooccur in virtually all known patients. Hinton and Shallice (1991) replicated the cooccurrence of visual and semantic errors by lesioning a recurrent connectionist network trained to map from orthography to semantics. While the success of their simulations is encouraging, there is little understanding of what underlying principles are responsible for them. In this paper we evaluate and, where possible, improve on the most important design decisions made by Hinton and Shallice, relating to the task, the network architecture, the training procedure, and the testing procedure. We identify four properties of networks that underly their ability to reproduce the deep dyslexic symptomcomplex: distributed orthographic and semantic representations, gradient descent learning, attractors for word meanings, and greater richness of concrete vs. abstract semantics. The first three of these are general connectionist principles and the last is based on earlier theorizing. Taken together, the results demonstrate the usefulness of a connectionist approach to understanding deep dyslexia in particular, and the viability of connectionist neuropsychology in general.
Nonlinear BlackBox Modeling in System Identification: a Unified Overview
 Automatica
, 1995
"... A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, ..."
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Cited by 141 (15 self)
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A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping from observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function e...