BALSON: Bayesian Least Squares Optimization with Nonnegative L1-Norm Constraint
This work addresses parameter reconstruction in fitting problems for researchers in statistics or machine learning, but it appears incremental as it builds on existing Bayesian and sampling techniques.
The paper tackles the problem of parameter estimation with nonnegative L1-norm constraints by proposing BALSON, a Bayesian approach that approximates the posterior distribution using Dirichlet distributions and sampling methods, resulting in better performance than conventional methods in polynomial fitting problems.
A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-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 L1-norm constraint of the parameters, we further approximate the true posterior distribution by a Dirichlet distribution. We estimate the statistics of the approximating Dirichlet posterior distribution by sampling methods. Four sampling methods have been introduced. 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.