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.
Least-square support vector machines（LS-SVM） are applied for learning the chaotic behavior of Chua＇s circuit.The system is divided into three multiple-input single-output（MISO） structures and the LS-SVM are trained individually.Comparing with classical approaches,the proposed one reduces the structural complexity and the selection of parameters is avoided.Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation.Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua＇s circuit state variables,and exhibit the chaotic attractors under the autonomous working mode.
