BALSON: BAYESIAN LEAST SQUARES OPTIMIZATION WITH NONNEGATIVE L1-NORM CONSTRAINT

Abstract

A Bayesian approach termed the BAyesian Least Squares Optimization with Nonnegative L-1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be a Dirichlet distribution. With the Bayes rule, searching for the optimal parameters is equivalent to finding the mode of the posterior distribution. In order to explicitly characterize the nonnegative L-1-norm constraint of the parameters, we further approximate the true posterior distribution by a Dirichlet distribution. We estimate the moments of the approximated Dirichlet posterior distribution by sampling methods. Four sampling methods have been introduced and implemented. With the estimated posterior distributions, the original parameters can be effectively reconstructed in polynomial fitting problems, and the BALSON framework is found to perform better than conventional methods.