Abstract

Mixture models have been widely used as a statistical learning paradigm in various unsupervised machine learning applications, where labeling a vast amount of data is impractical and costly. They have shown a significant success and encouraging performance in many real-world problems from different fields such as computer vision, information retrieval and pattern recognition. One of the most widely used distributions in mixture models is Gaussian distribution, due to its characteristics, such as its simplicity and fitting capabilities. However, data obtained from some applications could have different properties like non-Gaussian and asymmetric nature.
In this thesis, we propose multivariate Beta mixture models which offer flexibility, various shapes with promising attributes. These models can be considered as decent alternatives to Gaussian distributions.
We explore multiple Bayesian inference approaches for multivariate Beta mixture models and propose a suitable solution for the problem of estimating parameters using Markov Chain Monte Carlo (MCMC) technique. We exploit Gibbs sampling within Metropolis-Hastings for learning parameters of our finite mixture model. Moreover, a fully Bayesian approach based on birth-death MCMC technique is proposed which simultaneously allows cluster assignments, parameters estimation and the selection of the optimal number of clusters. Finally, we develop a nonparametric Bayesian framework by extending our finite mixture model to infinity using Dirichlet process to tackle the model selection problem. Experimental results obtained from challenging applications (e.g., intrusion detection, medical, etc.) confirm that our proposed frameworks can provide effective solutions comparing to existing alternatives.