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Communicated by Gerald Tesauro Statistical Theory of Learning Curves under Entropic Loss Criterion
"... The present paper elucidates a universal property of learning curves, which shows how the generalization error, training error, and the complexity of the underlying stochastic machine are related and how the behavior of a stochastic machine is improved as the number of training examples increases. ..."
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. The error is measured by the entropic loss. It is proved that the generalization error converges to Ho, the entropy of the conditional distribution of the true machine, as HO + m* / (2 t), while the training error converges as HO m'/(2t) , where t is the number of examples and m ' shows
Blind Signal Separation: Statistical Principles
, 2003
"... Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mut ..."
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Cited by 522 (4 self)
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Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mutual independence between the signals. The weakness of the assumptions makes it a powerful approach but requires to venture beyond familiar second order statistics. The objective of this paper is to review some of the approaches that have been recently developed to address this exciting problem, to show how they stem from basic principles and how they relate to each other.
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Multiobjective Evolutionary Algorithms: Analyzing the StateoftheArt
, 2000
"... Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mideighties in an attempt to stochastically solve problems of this generic class. During the past decade, ..."
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Cited by 424 (7 self)
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Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mideighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of c...
Visual Recognition of American Sign Language Using Hidden Markov Models
, 1995
"... Using hidden Markov models (HMM's), an unobstrusive single view camera system is developed that can recognize hand gestures, namely, a subset of American Sign Language (ASL). Previous systems have concentrated on finger spelling or isolated word recognition, often using tethered electronic glov ..."
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Cited by 346 (14 self)
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Using hidden Markov models (HMM's), an unobstrusive single view camera system is developed that can recognize hand gestures, namely, a subset of American Sign Language (ASL). Previous systems have concentrated on finger spelling or isolated word recognition, often using tethered electronic gloves for input. We achieve high recognition rates for full sentence ASL using only visual cues. A forty word lexicon consisting of personal pronouns, verbs, nouns, and adjectives is used to create 494 randomly constructed five word sentences that are signed by the subject to the computer. The data is separated into a 395 sentence training set and an independent 99 sentence test set. While signing, the 2D position, orientation, and eccentricity of bounding ellipses of the hands are tracked in real time with the assistance of solidly colored gloves. Simultaneous recognition and segmentation of the resultant stream of feature vectors occurs five times faster than real time on an HP 735. With a strong ...
Entropic Priors
, 1991
"... : Entropic priors assign probabilities by combining in an inseparable way the information theoretic concept of entropy with the underlying Riemannian geometry of the hypothesis space. These priors form the cornerstone of a developing new and more objective Bayesian theory of inference. Contents 1 I ..."
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Cited by 7 (0 self)
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: Entropic priors assign probabilities by combining in an inseparable way the information theoretic concept of entropy with the underlying Riemannian geometry of the hypothesis space. These priors form the cornerstone of a developing new and more objective Bayesian theory of inference. Contents 1
Exponentiated Gradient Versus Gradient Descent for Linear Predictors
 Information and Computation
, 1995
"... this paper, we concentrate on linear predictors . To any vector u 2 R ..."
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Cited by 325 (14 self)
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this paper, we concentrate on linear predictors . To any vector u 2 R
Entropic Priors
, 1991
"... Abstract: Entropic priors assign probabilities by combining in an inseparable way the information theoretic concept of entropy with the underlying Riemannian geometry of the hypothesis space. These priors form the cornerstone of a developing new and more objective Bayesian theory of inference. ..."
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Abstract: Entropic priors assign probabilities by combining in an inseparable way the information theoretic concept of entropy with the underlying Riemannian geometry of the hypothesis space. These priors form the cornerstone of a developing new and more objective Bayesian theory of inference.
An Entropic Estimator for Structure Discovery
, 1999
"... We introduce a novel framework for simultaneous structure and parameter learning in hiddenvariable conditional probability models, based on an entropic prior and a solution for its maximum a posteriori (MAP) estimator. The MAP estimate minimizes uncertainty in all respects: crossentropy between mo ..."
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Cited by 41 (0 self)
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We introduce a novel framework for simultaneous structure and parameter learning in hiddenvariable conditional probability models, based on an entropic prior and a solution for its maximum a posteriori (MAP) estimator. The MAP estimate minimizes uncertainty in all respects: crossentropy between
Correlationbased feature selection for machine learning
, 1998
"... A central problem in machine learning is identifying a representative set of features from which to construct a classification model for a particular task. This thesis addresses the problem of feature selection for machine learning through a correlation based approach. The central hypothesis is that ..."
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Cited by 297 (3 self)
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A central problem in machine learning is identifying a representative set of features from which to construct a classification model for a particular task. This thesis addresses the problem of feature selection for machine learning through a correlation based approach. The central hypothesis is that good feature sets contain features that are highly correlated with the class, yet uncorrelated with each other. A feature evaluation formula, based on ideas from test theory, provides an operational definition of this hypothesis. CFS (Correlation based Feature Selection) is an algorithm that couples this evaluation formula with an appropriate correlation measure and a heuristic search strategy. CFS was evaluated by experiments on artificial and natural datasets. Three machine learning algorithms were used: C4.5 (a decision tree learner), IB1 (an instance based learner), and naive Bayes. Experiments on artificial datasets showed that CFS quickly identifies and screens irrelevant, redundant, and noisy features, and identifies relevant features as long as their relevance does not strongly depend on other features. On natural domains, CFS typically eliminated well over half the features. In most cases, classification accuracy using the reduced feature set equaled or bettered accuracy using the complete feature set.
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