Research On Exact Inference And Sampling Based Approximate Inference Methods Of Nonparametric Bayesian Model

Probabilistic graph models are one of the most essential statistical machine learning models in the field of artificial intelligence.They are widely used in the fields of personal credit risk assessment,natural language processing,biomedicine,etc.Non-parametric Bayesian model is a special kind of them.Non-parametric Bayesian model belongs to a more complex category because it has the dual characteristics of nonparametric model and Bayesian model.But its model complexity is high,the research is difficult,especially in the model structure,model size and distribution function of non-parametric model can vary with the change of observed data,and the number of model parameters can grow with the increase of sample size.As a result,it is difficult to determine the distribution function and increase the difficulty of distribution sampling in machine learning.This dissertation,based on the above characteristics of the non-parametric Bayesian model,analyzes the characteristics of its probability distribution function so as to conduct the exact inference and approximate inference research of the model.Theoretically,the probabilistic inference method proposed in this dissertation is applicable to the general probabilities of nonparametric Bayesian models with any number of observation samples,and has universality and generality.The gist and innovations of this study are as follows:Aiming at the problem that it is for the finite dimensional observation samples of the nonparametric Bayesian model generated by the stick breaking construction method,it is difficult to determine the number of rounds generated by each sample and thus unable to identify its distribution function,(that is,the number of rounds and distribution function of each sample cannot be determined because there may be any round containing one sample between two samples).A one-for-all method is proposed to directly marginalize all the unobservable variables such as the number of rounds in which each sample is located and the size of each round to quickly obtain the distribution function that the observed values of k random variables obey.Based on the conjugacy between the distribution functions of random variables,the joint probability likelihood functions containing all the observed samples are obtained.A unified likelihood analysis framework for the stick breaking construction method of all nonparametric Bayesian models with arbitrary finite random variables is theoretically established.In order to solve the problem that the sequence samples need to be constructed in the process of sampling finite dimensional observation samples of nonparametric Bayesian model by using the stick breaking construction method,a simple approximate sampling method for the distribution of Beta process is proposed,which uses the relationship between the properties of Beta process and Dirichlet process.According to the splitting and normalizing properties of the Dirichlet distribution,an approximate Beta process distribution sample result is obtained.By analyzing the sampling mechanism of a single sample,a framework is established to repeat this sampling method any number of times to perform a sequential sampling of any finite number of Beta process random variables.In view of the complexity of the two steps needed to complete the sampling of Gamma process distribution and Poisson distribution respectively when sampling the Gamma Poisson process distribution function,a Gamma Poisson process distribution sampling method based on the properties of Gamma process distribution and Poisson distribution is proposed.For each sample taken using this method,an integer matrix of arbitrary dimensions can be obtained.A framework of approximate inference for the distribution function of the obtained samples is established by using sampling method in the infinite dimensional Gamma Poisson process.In order to solve the problem that the definition form of Beta process factor analysis model is too complicated to calculate the observation samples,a method of generating Beta process factor analysis model observation is proposed by using matrix analysis method to transform vector dot product operation into matrix multiplication operation.The calculation results of observation samples in simplified definition form of Beta process factor analysis model are obtained.This method can be applied to some important fields such as factorization and factor analysis.