Automated Model Selection (AMS) on Finite Mixtures: A Theoretical Analysis

From the Bayesian Ying-Yang (BYY) harmony learning theory, a harmony function has been developed for finite mixtures with a novel property that its maximization can make model selection automatically during parameter learning. In this paper, we make a theoretical analysis on the harmony function and prove that the global maximization of the harmony function leads to the automated model selection property when there is no or weak overlap between the actual components in the sample data. Moreover, it is proved that the estimates of the parameters through maximizing the harmony function are generally biased, but the deviation error is dominated by the average overlap measure between the actual components in the mixture.