This paper proposes a novel approach, Markov Chain Monte Carlo (MCMC) sampling approximation, to deal with intractable high-dimension integral in the evidence framework applied to Support Vector Regression (SVR). Unli...This paper proposes a novel approach, Markov Chain Monte Carlo (MCMC) sampling approximation, to deal with intractable high-dimension integral in the evidence framework applied to Support Vector Regression (SVR). Unlike traditional variational or mean field method, the proposed approach follows the idea of MCMC, firstly draws some samples from the posterior distribution on SVR's weight vector, and then approximates the expected output integrals by finite sums. Experimental results show the proposed approach is feasible and robust to noise. It also shows the performance of proposed approach and Relevance Vector Machine (RVM) is comparable under the noise circumstances. They give better robustness compared to standard SVR.展开更多
This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence re...This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q) nonlinear regression models.展开更多
An approach was proposed for optimizing beamforming that was based on Support Vector Regression (SVR). After studying the mathematical principal of the SVR algorithm and its primal cost function, the modified cost fun...An approach was proposed for optimizing beamforming that was based on Support Vector Regression (SVR). After studying the mathematical principal of the SVR algorithm and its primal cost function, the modified cost function was first applied to uniform array beamforming, and then the corresponding parameters of the beamforming were optimized. The framework of SVR uniform array beamforming was then established. Simulation results show that SVR beamforming can not only approximate the performance of conventional beamforming in the area without noise and with small data sets, but also improve the generalization ability and reduce the computation burden. Also, the side lobe level of both linear and circular arrays by the SVR algorithm is improved sharply through comparison with the conventional one. SVR beamforming is superior to the conventional method in both linear and circular arrays, under single source or double non-coherent sources.展开更多
This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on th...This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].展开更多
基金Supported by the National Natural Science Foundation of China (No. 60972106, 61072103)China Postdoctoral Science Foundation (No. 20090450750)
文摘This paper proposes a novel approach, Markov Chain Monte Carlo (MCMC) sampling approximation, to deal with intractable high-dimension integral in the evidence framework applied to Support Vector Regression (SVR). Unlike traditional variational or mean field method, the proposed approach follows the idea of MCMC, firstly draws some samples from the posterior distribution on SVR's weight vector, and then approximates the expected output integrals by finite sums. Experimental results show the proposed approach is feasible and robust to noise. It also shows the performance of proposed approach and Relevance Vector Machine (RVM) is comparable under the noise circumstances. They give better robustness compared to standard SVR.
文摘This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q) nonlinear regression models.
基金the Foundation of Returned Scholar of Shaanxi Province(SLZ2008006)
文摘An approach was proposed for optimizing beamforming that was based on Support Vector Regression (SVR). After studying the mathematical principal of the SVR algorithm and its primal cost function, the modified cost function was first applied to uniform array beamforming, and then the corresponding parameters of the beamforming were optimized. The framework of SVR uniform array beamforming was then established. Simulation results show that SVR beamforming can not only approximate the performance of conventional beamforming in the area without noise and with small data sets, but also improve the generalization ability and reduce the computation burden. Also, the side lobe level of both linear and circular arrays by the SVR algorithm is improved sharply through comparison with the conventional one. SVR beamforming is superior to the conventional method in both linear and circular arrays, under single source or double non-coherent sources.
基金Supported by the NSSFC(02BTJ001) Supported by the NSSFC(04BTJ002) Supported by the Grant for Post-Doctorial Fellows in Southeast University
文摘This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].
