The classical stochastic approximation methods are shown to yield algorithms to solve several formulations of the PAC learning problem defined on the domain [0,1](d). Under some smoothness conditions on the probability measure functions, simple algorithms to solve some PAC learning problems are proposed based on networks of nonpolynomial units (e.g. artificial neural networks). Conditions on the sizes of the samples required to ensure the error bounds are derived using martingale inequalities.

We present two classes of convergent algorithms for learning continuous functions and regressions that are approximated by feedforward networks. The first class of algorithms, applicable to networks with unknown weights located only in the output layer, is obtained by utilizing the potential function methods of Aizerman et al. (1970). The second class, applicable to general feedforward networks, is obtained by utilizing the classical Robbins-Monro style stochastic approximation methods (1951). Conditions relating the sample sizes to the error bounds are derived for both classes of algorithms using martingale-type inequalities. For concreteness, the discussion is presented in terms of neural networks, but the results are applicable to general feedforward networks, in particular to wavelet networks. The algorithms can be directly adapted to concept learning problems.

Given two subsets S/sub 1/ and S/sub 2/ (not necessarily finite) of /spl Rfr//sup d/ separable by a Boolean combination of learning half-spaces, the authors consider the problem of (in the sense of Valiant) the separation function from a finite set of examples, i.e., they produce with a high probability a function close to the actual separating function. The authors' solution consists of a system of N perceptrons and a single consolidator which combines the outputs of the individual perceptrons; it is shown that an off-line version of this problem, where the examples are given in a batch, can be solved in time polynomial in the number of examples. The authors also provide an on-line learning algorithm that incrementally solves the problem by suitably training a system of N perceptrons much in the spirit of the classical perceptron learning algorithm.>

A system of probably and approximately correct learners of Valiant type that infer concepts from a sample is considered. Each learner had been trained by a sample using the methods of minimizing the empirical error, and no examples are available to the fuser. A majority fuser is known to make the composite system better than the best of the learners in terms of normalized confidence (that corresponds to the same precision value). An analysis of general majority fusers is carried out to obtain bounds on actual and expected errors. Conditions under which the r of N fuser performs better, in terms of normalized confidence or precision, than best of the individual learners are obtained. For a special class of statistically independent learners, slightly weaker conditions are obtained. Two fusers that use the location information of a test point are proposed, and are shown to be better than a learner with least empirical error.>

Given N learners each capable of learning concepts (subsets) in the sense of Valiant (1985), we are interested in combining them using a single fuser. We consider two cases. In open fusion the fuser is given the sample and the hypotheses of the individual learners; we show that a fusion rule can be obtained by formulating this problem as another learning problem. We show sufficiency conditions that ensure the composite system to be better than the best of the individual. Second, in closed fusion the fuser does not have an access to either the training sample or the hypotheses of the individual learners. By using a linear threshold fusion function (of the outputs of individual learners) we show that the composite system can be made better than the best of the statistically independent learners.>

Article Free Access Share on Hybrid pattern recognition system capable of self-modification Authors: Charles W. Glover Intelligent Systems Section, Center for Engineering Systems Advanced Research, Oak Ridge National Laboratory, Oak Ridge, TN Intelligent Systems Section, Center for Engineering Systems Advanced Research, Oak Ridge National Laboratory, Oak Ridge, TNView Profile , Nageswara S. V. Rao Intelligent Systems Section, Center for Engineering Systems Advanced Research, Oak Ridge National Laboratory, Oak Ridge, TN Intelligent Systems Section, Center for Engineering Systems Advanced Research, Oak Ridge National Laboratory, Oak Ridge, TNView Profile , E. M. Oblow Intelligent Systems Section, Center for Engineering Systems Advanced Research, Oak Ridge National Laboratory, Oak Ridge, TN Intelligent Systems Section, Center for Engineering Systems Advanced Research, Oak Ridge National Laboratory, Oak Ridge, TNView Profile Authors Info & Claims CIKM '93: Proceedings of the second international conference on Information and knowledge managementDecember 1993 Pages 239–244https://doi.org/10.1145/170088.170140Published:01 December 1993Publication History 0citation362DownloadsMetricsTotal Citations0Total Downloads362Last 12 Months3Last 6 weeks3 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Given two subsets S/sub 1/ and S/sub 2/ (not necessarily finite) of R/sup d/ separable by a Boolean combination of N halfspaces, the authors consider the problem of learning the separation function from a finite set of examples. The solution consists of a system of N perceptrons and a single consolidator which combines the outputs of the individual perceptrons. The authors show that an off-line version of this problem where the examples are given in a batch, can be solved in time polynomial in the number of examples. The authors also provide an on-line learning algorithm that incrementally solves the problem by suitably training a system of N perceptrons much in the spirit of classical perceptron learning algorithm.>

Given N learners each capable of learning concepts (subsets) in the sense of Valiant (1985), we are interested in combining them using a single fuser. We consider two cases. In open fusion the fuser is given the sample and the hypotheses of the individual learners; we show that a fusion rule can be obtained by formulating this problem as another learning problem. We show sufficiency conditions that ensure the composite system to be better than the best of the individual. Second, in closed fusion the fuser does not have an access to either the training sample or the hypotheses of the individual learners. By using a linear threshold fusion function (of the outputs of individual learners) we show that the composite system can be made better than the best of the statistically independent learners. >

A methodology has been developed for the treatment of systematic errors that arise in the processing of sparse sensor data. A detailed application of this methodology to the construction, from wide-angle sonar sensor data, of navigation maps for use in autonomous robotic navigation is presented. In the methodology, a four-valued labeling scheme and a simple logic for label combination are introduced. The four labels Conflict, Occupied, Empty, and Unknown are used to mark the cells of the navigation maps. The logic allows for the rapid updating of these maps as new information is acquired. Systematic errors are treated by relabeling conflicting pixel assignments. Most of the new labels are obtained from analyses of the characteristic patterns of conflict that arise during the information processing. The remaining labels are determined by imposing an elementary consistent-labeling condition.>

This article extends Operator-Uncertainty Theory (OT) to the problem of uncertainty propagation in logical inferencing systems. the OT algebra and propositional interpretations presented in previous articles are applied here to derive operators for logical inferencing in the presence of conflict and undecidability. Operators for propagating uncertainties through the logical operations of disjunction and conjunction are defined. In addition, new OT operators for implication, modus ponens and modus tollens, are also proposed. the operators derived using the OT methodology are found to give rise to a four-valued logic similar to that used in computer circuit design. This framework allows uncertainty in inferencing to be represented in the form of rules convenient for use in expert systems as well as logical networks. the theory is general enough to deal with questions of conflict and undecidability, and to propagate their effects through the most widely used inference operations.