Correcting Boosted Mixture Learning method using Vuong's test and its application in the Gamma Mixture Model‎

‎The boosted mixture learning method‎, ‎BML‎, ‎is an incremental method to learn mixture models for the classification problem‎. ‎In each step of the boosted mixture learning method‎, ‎a new component is added to the mixture model according to an objective function to ensure that the objective function is maximized‎. ‎Sometimes the likelihood function or equivalently information criteria are defined as the objective function of BML‎. ‎The mixture model is updated whenever a new component is added to the mixture model based on the maximum likelihood function and information criteria‎.

‎Since the information criteria does not have the ability to identify equivalent models‎, ‎therefore‎, ‎it is possible that the new mixture model and the current mixture model are equivalent‎.

‎In this paper‎, ‎the boosted mixture learning method has been corrected using Vuong's model selection test‎, ‎which has the ability to identify equivalent models‎. ‎The performance of two learning methods is evaluated over simulation data and over the U.S‎. ‎imports of goods by customs basis.‎