Variational Bayesian inference for a Dirichlet process mixture of beta distributions and application

Finite beta mixture model (BMM) has been shown to be very flexible and powerful for bounded support data modeling. However, BMM cannot automatically select the proper number of the mixture components based on the observed data, which is important and has a deterministic effect on the modeling accuracy. In this paper, we aim at tackling this problem by infinite Beta mixture model (InBMM). It is based on the Dirichlet process (DP) mixture with the assumption that the number of the mixture components is infinite in advance and can be automatically determined according to the observed data. Further, a variational InBMM using single lower-bound approximation (VBInBMM) is proposed which applies the stick-breaking representation of the DP and is learned by an extended variational inference framework. Numerical experiments on both synthetic and real data, generated from two challenging application namely image categorization and object detection, demonstrate good performance obtained by the proposed method.