Bayesian probability

Physics

Pattern recognition (psychology)

Dirichlet distribution

Overfitting

Inference

Feature (linguistics)

Dirichlet process

Mathematics

Latent Dirichlet allocation

Evolutionary biology

Biology

Algorithm

Mathematical optimization

Gaussian

Mathematical analysis

Philosophy

Function (biology)

Boundary value problem

Artificial intelligence

Bayesian inference

Topic model

Computer science

Linguistics

Gaussian process

Quantum mechanics

Applied mathematics

Artificial neural network

Mixture model

IEEE Transactions on Neural Networks and Learning Systems

In this paper, we develop a novel variational Bayesian learning 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 EVI framework. In principle, the proposed model can be viewed as an infinite inverted Dirichlet mixture model that allows the automatic determination of the number of mixture components from data. Therefore, the problem of predetermining the optimal number of mixing components has been overcome. Moreover, the problems of overfitting and underfitting are avoided by the Bayesian estimation approach. Compared with several recently proposed DP-related methods and conventional applied methods, the good performance and effectiveness of the proposed method have been demonstrated with both synthesized data and real data evaluations.

Variational Bayesian Learning for Dirichlet Process Mixture of Inverted Dirichlet Distributions in Non-Gaussian Image Feature Modeling