Infinite Mixture of Inverted Dirichlet Distributions
This work addresses the challenge of pre-determining optimal mixture components for positive data modeling, which is incremental as it builds on existing Dirichlet process and variational inference methods.
The authors tackled the problem of modeling vectors with positive elements by developing a Bayesian estimation method for a Dirichlet process mixture of inverted Dirichlet distributions, which automatically determines the number of mixture components and avoids over-fitting and under-fitting, demonstrating good performance in evaluations.
In this work, we develop a novel Bayesian estimation method for the Dirichlet process (DP) mixture of the inverted Dirichlet distributions, which has been shown to be very flexible for modeling vectors with positive elements. The recently proposed extended variational inference (EVI) framework is adopted to derive an analytically tractable solution. The convergency of the proposed algorithm is theoretically guaranteed by introducing single lower bound approximation to the original objective function in the VI framework. In principle, the proposed model can be viewed as an infinite inverted Dirichelt mixture model (InIDMM) that allows the automatic determination of the number of mixture components from data. Therefore, the problem of pre-determining the optimal number of mixing components has been overcome. Moreover, the problems of over-fitting and under-fitting are avoided by the Bayesian estimation approach. Comparing with several recently proposed DP-related methods, the good performance and effectiveness of the proposed method have been demonstrated with both synthesized data and real data evaluations.