Dirichlet Process Mixture Model Based Nonparametric Bayesian Modeling and Variational Inference

Abstract

Nonparametric Bayesian modeling receive a great deal of attention in last decades. Dirichlet Process Mixture Model (DPMM) based soft sensing model is developed where the number of parameters can be determined automatically based on the given data. The core task in nonparametric Bayesian modeling is the posterior inference. A novel variational inference algorithm is proposed to determine the posterior distribution. In this variational inference approach, the gradient computation of optimization is derived by Monte Carlo sampling which is not restricted to the specific model expression. To address the challenge of gradient computing, black box Monte Carlo sampling method is also used. To illustrate the effectiveness, the proposed methodology is demonstrated in a practical polypropylene producing process.