The infinite Student's t-mixture for robust modeling

Finite mixture models have been widely used for modeling probability distribution of real data sets due to its benefits from analytical tractability. Among the finite mixtures, the finite Student's t-mixture model (SMM) are tolerant to the untypical data (outliers). However, the SMM could not automatically determine the proper number of components, which is important and may has a significant effect on the learned model. In this paper, we propose an infinite Student's t-mixture model (iSMM) to handle this issue. This model is based on the Dirichlet process mixture which assumes the number of components in a mixture is infinite in advance, and determines the appropriate value of this number according to the observed data. Moreover, we derive an efficient variational Bayesian inference algorithm for the proposed model. Through applications in blind signal detection and image segmentation, it is shown that the iSMM possesses the advantages of both the Student's t-distribution and the Dirichlet process mixture, offering a more powerful and robust performance than competing models.

► We propose the infinite Student's t-mixture model.
► We derive an efficient variational Bayesian inference algorithm for this model.
► This model is applied to the problems of blind signal detection and image segmentation.
► This model can determine the proper number of components and robust to outliers.