Topic
Statistical learning theory
About: Statistical learning theory is a research topic. Over the lifetime, 1618 publications have been published within this topic receiving 158033 citations.
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16 Aug 2006
TL;DR: A novel method of fuzzy compensation multi-class support vector machine, named as FC-SVM, is proposed in this paper, which imports a fuzzy compensation function to the penalty in the straightly construction multi- class SVM classification problem proposed by Weston and Watkins.
Abstract: Support vector machine (SVM), proposed by Vapnik based on statistical learning theory, is a novel machine learning method. However, there are two problems to be solved in this field: one is the multi-class classification problem, and the other is the sensitivity to the noisy data. In order to overcome these difficulties, a novel method of fuzzy compensation multi-class support vector machine, named as FC-SVM, is proposed in this paper. This method imports a fuzzy compensation function to the penalty in the straightly construction multi-class SVM classification problem proposed by Weston and Watkins. Aim at the dual affects to classification results by each input data, this method has punish item be fuzzy, compensates weight to classification, reconstructs the optimization problem and its restrictions, reconstructs Langrage formula, and presents the theories deduction. This method is applied to the benchmark data sets. The experiment presents our method is feasible.
5 citations
Posted Content•
TL;DR: This work provides two natural notions of learnability of a function class under a general stochastic process and shows that the second one is in fact equivalent to online learnability.
Abstract: Statistical learning theory under independent and identically distributed (iid) sampling and online learning theory for worst case individual sequences are two of the best developed branches of learning theory. Statistical learning under general non-iid stochastic processes is less mature. We provide two natural notions of learnability of a function class under a general stochastic process. We show that both notions are in fact equivalent to online learnability. Our results are sharpest in the binary classification setting but we also show that similar results continue to hold in the regression setting.
5 citations
25 May 2003
TL;DR: GiniSVM, a support vector machine kernel-based classifier based on quadratic entropy, is shown to encode the sensor data with maximum fidelity for a given constraint on transmission budget, and a classifier architecture that implements these principles is presented.
Abstract: Wireless smart sensors impose severe power constraints that call for power budget optimization at all levels in the design hierarchy. We elucidate a connection between statistical learning theory and rate distortion theory that allows to operate a wireless sensor array at fundamental limits of power dissipation. GiniSVM, a support vector machine kernel-based classifier based on quadratic entropy, is shown to encode the sensor data with maximum fidelity for a given constraint on transmission budget. The transmission power is minimized by GiniSVM in the form of a quadratic cost function under linear constraints. A classifier architecture that implements these principles is presented.
5 citations
01 Jan 2005
TL;DR: The potential of the issue of regularization in identification of Hammerstein systems in the context of primal-dual kernel machines and Least Squares Support Vector Machines is discussed and an extension of the Hammerstein class to finite order Volterra series and methods resulting in structure detection are proposed.
Abstract: Model complexity control and regularization play a crucial role in statistical learning theory and also for problems in system identification. This text discusses the potential of the issue of regularization in identification of Hammerstein systems in the context of primal-dual kernel machines and Least Squares Support Vector Machines (LS-SVMs) and proposes an extension of the Hammerstein class to finite order Volterra series and methods resulting in structure detection.
5 citations
25 May 2004
TL;DR: A versatile statistical verification methodology is presented that is applied to finding verifiably safe flight envelopes for a class of maneuvers and compared with other statistical techniques used for estimating execution times and controller performance.
Abstract: We present a versatile statistical verification methodology and we illustrate different uses of this methodology on two examples of nonlinear real-time UAV controllers. The first example applies our statistical methodology to the verification of a computation time property for a software implementation of a high-performance controller as a function of controller state variable values. The second example illustrates our statistical verification methodology applied to finding verifiably safe flight envelopes for a class of maneuvers, again as a function of controller state variable values. We compare our approach to verification with other statistical techniques used for estimating execution times and controller performance. We close with candidate topics for future work.
5 citations