Variational bayes learning for models with linear equality constraints

It is normal that the model and parameters with constraint in machine learning field. Relative to constraints methods based on maximum likelihood criterion, We present a method to approximate the posterior probability of parameters, which are with linear constraints in variational Bayesian framework. We first eliminate the equality constraints with parameters transformation method, and then use variational learning process to approximate the posterior probability of parameters. Finally, we verify that the proposed method can effectively approximate the posterior probability of parameters through a simple linear regression example.