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.

Safe Learning-Based Control of Stochastic Jump Linear Systems: a Distributionally Robust Approach.

Abstract: We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of i.i.d. observations. We adopt a distributionally robust approach to compute a mean-square stabilizing feedback gain with a given probability. The larger the sample size, the less conservative the controller, yet our methodology gives stability guarantees with high probability, for any number of samples. Using tools from statistical learning theory, we estimate confidence regions for the unknown probability distributions (ambiguity sets) which have the shape of total variation balls centered around the empirical distribution. We use these confidence regions in the design of appropriate distributionally robust controllers and show that the associated stability conditions can be cast as a tractable linear matrix inequality (LMI) by using conjugate duality. The resulting design procedure scales gracefully with the size of the probability space and the system dimensions. Through a numerical example, we illustrate the superior sample complexity of the proposed methodology over the stochastic approach.

Theory and application of support vector machine

Abstract: Support vector machine is a new kind of machine learning method.Because of its excellent learning performance,this technology has become the new research hotspot in the field of international machine learning.Introduces the statistical learning theory and support vector machine based on this theory,states in brief the present application situation of support vector machine,points out some problems existing in support vector machine research and further research direction.

The Link Between Statistical Learning Theory and Econometrics: Applications in Economics, Finance, and Marketing

Abstract: Statistical Learning refers to statistical aspects of automated extraction of regularities (structure) in datasets. It is a broad area which includes neural networks, regression-trees, nonparametric statistics and sieve approximation, boosting, mixtures of models, computational complexity, computational statistics, and nonlinear models in general. Although Statistical Learning Theory and Econometrics are closely related, much of the development in each of the areas is seemingly proceeding independently. This special issue brings together these two areas, and is intended to stimulate new applications and appreciation in economics, finance, and marketing. This special volume contains ten innovative articles covering a broad range of relevant topics.

A Classification of Remote Sensing Image Based on Improved Compound Kernels of Svm

Abstract: The accuracy of RS classification based on SVM which is developed from statistical learning theory is high under small number of train samples, which results in satisfaction of classification on RS using SVM methods. The traditional RS classification method combines visual interpretation with computer classification. The accuracy of the RS classification, however, is improved a lot based on SVM method, because it saves much labor and time which is used to interpret images and collect training samples. Kernel functions play an important part in the SVM algorithm. It uses improved compound kernel function and therefore has a higher accuracy of classification on RS images. Moreover, compound kernel improves the generalization and learning ability of the kernel.