  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.
