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.

Time-Frequency Learning Machines

Abstract: Over the last decade, the theory of reproducing kernels has made a major breakthrough in the field of pattern recognition. It has led to new algorithms, with improved performance and lower computational cost, for nonlinear analysis in high dimensional feature spaces. Our paper is a further contribution which extends the framework of the so-called kernel learning machines to time-frequency analysis, showing that some specific reproducing kernels allow these algorithms to operate in the time-frequency domain. This link offers new perspectives in the field of non-stationary signal analysis, which can benefit from the developments of pattern recognition and statistical learning theory.

Research of granular support vector machine

Abstract: Granular support vector machine (GSVM) is a new learning model based on Granular Computing and Statistical Learning Theory. Compared with the traditional SVM, GSVM improves the generalization ability and learning efficiency to a large extent. This paper mainly reviews the research progress of GSVM. Firstly, it analyzes the basic theory and the algorithm thought of GSVM, then tracking describes the research progress of GSVM including the learning model and specific applications in recent years, finally points out the research and development prospects.

Simulated Annealing: Rigorous finite-time guarantees for optimization on continuous domains

Abstract: Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Least square support vector machine and relevance vector machine for evaluating seismic liquefaction potential using SPT

Abstract: The determination of liquefaction potential of soil is an imperative task in earthquake geotechnical engineering. The current research aims at proposing least square support vector machine (LSSVM) and relevance vector machine (RVM) as novel classification techniques for the determination of liquefaction potential of soil from actual standard penetration test (SPT) data. The LSSVM is a statistical learning method that has a self-contained basis of statistical learning theory and excellent learning performance. RVM is based on a Bayesian formulation. It can generalize well and provide inferences at low computational cost. Both models give probabilistic output. A comparative study has been also done between developed two models and artificial neural network model. The study shows that RVM is the best model for the prediction of liquefaction potential of soil is based on SPT data.