Research On The Extended Variational Inference Methods For The Non-Gaussian Statistical Models

The finite mixture models have become an important kind of data modeling tools in statistical machine learning due to their strong fitting ability to data.They have many application prospects in the fields of pattern recognition,computer vision and data mining.However,the traditional finite mixture models are mainly constructed by Gaussian distributions,which make them unable to describe some special data generated in real life,such as bounded data and asymmetric data.Therefore,it is urgent to use some finite mixture models constructed by non-Gaussian distributions to solve the above problems.Among these non-Gaussian mixture models,the inverted Beta-Liouville mixture models have been widely studied because of their good modeling ability for positive vector data.However,the traditional training methods of the finite mixture models,such as expectation maximization algorithm and Markov chain Monte Carlo method,have great shortcomings and,therefore,cannot be used to train the inverted Beta-Liouville mixture models and solve practical problems.In order to cope with the problems mentioned above,this paper proposes a complete variational inference framework for the inverted Beta-Liouville mixture models.This framework can solve the problems of parameter estimation and model selection exist in the model training phase simultaneously,so that the models can be effectively applied to solve parctical problems.In view of the rapid growth of data in the era of big data,this paper further improves the proposed variational inference framework and puts forward the stochastic variational inference framework for the inverted Beta-Liouville mixture models.This framework can solve the problems exposed by the traditional variational inference framework under big data,and shows better performance.In order to verify the effectiveness and practical application value of the above two frameworks,this paper uses two real applications,namely,human motion recognition and goods detection to test the model and its related inference frameworks,and further compares them with the mainstream fully connected neural network.Experimental results show that the proposed two frameworks have good performance and great practical value.