Estimation Method Of Regular Parameter Based On Maximum Evidence

This article is in the context of signal processing,the relationship between the regular parameter and its distribution parameter is derived by constructing the Gibbs distribution corresponding to each part of the objective function in the op-timization problem based on Bayesian framework,among them,the distribution parameters are usually called hyperparameters,so that the estimation problem of the regular parameters in the optimization problem is transformed into the esti-mation problem of the hyperparameters.The method of evidence analysis in the hierarchical Bayesian model is used to estimate the hyperparameters.It's basic idea is to first integrate the model parameters to obtain the evidence of the hyperpa-rameters,and then maximize the evidence to estimate the hyperparameters.This method is called Maximize evidence.In order to obtain the evidence of hyperpa-rameters,the Laplace's approximation method is used to construct the approximate Gaussian distribution for the problem that the evidence is not integrable,so that the integration becomes possible.In practical applications,taking the sparse cod-ing problem as an example,the proposed evidence maximization method is used to estimate the regular parameter,and iteratively solved based on the EM algorithm,and finally a sparse coding problem solving algorithm based on maximum evidence is given.