Research On Tensor Decomposition Based On Parameter Estimation

Mixed model means that a large distribution is composed of multiple sub-distributions.E ach sub-distribution can be considered as an implicit variable which can not be directly observ ed but affect the value of the observed variables in the overall distribution.The parameter esti mation of mixed model is to mine the sub-distribution of the model making assumptions abo ut sub-distribution according to certain prior knowledge ahead and estimate the parameters of each sub-distribution according to the actual sample data.Traditional methods for solving par ameter estimation of mixed models are mainly divided into two categories:statistical learning algorithm and moment estimation.Statistical learning algorithms,such as Expected Maximu m(EM),use the idea of Maximum Likelihood Estimation(MLE)to iterate through two steps of "Maximum Likelihood" and "Expectation" and gradually approach the final solution value.Iterative computation of this kind of algorithm is easy to achieve,but it is easy to fall into loc al optimum.So scholars consider using moment estimation to solve this problem,mainly usin g sample moments to approximate the real moments of samples.The application of this metho d uses the concept of tensor.Tensor is the natural expansion of vector matrix in high-dimensi onal space.Vector has only one row of data(one-dimensional data),matrix has rows and colu mns(two-dimensional array),tensor is the form of multi-dimensional array.Tensors can be us ed to describe the complex functional correspondence among multiple variables because of th e data structure in high-dimensional space.In this paper,tensor decomposition is used to solve the parameter estimation problem of mixed model,which belongs to the category of moment estimation.The second and third mo ments are calculated from the sample data,and the parameters to be estimated are directly obt ained by tensor decomposition.Firstly,the basic concepts of tensor decomposition and mixed model are introduced,and the application of tensor decomposition in the field of parameter es timation of hybrid model is discussed later.Then,in order to improve the efficiency of tensor decomposition in solving mixed model parameters,the traditional tensor decomposition algori thm is combined with the idea of "divide and conquer",and the partitioned Tensor Decomposi tion(PTD)algorithm is proposed in this paper.The effectiveness of the algorithm is demonstr ated in detail through experiments.At the same time,this paper further designs and implemen ts the PTD algorithm based on Spark platform,which can meet the challenges of large-scale d ata in industry.The main contributions of this paper are as follows:(1)The anchor tensor.By sharing anchor tensors,a large tensor can be divided into sever al small sub-tensors.Each sub-tensor can be decomposed in parallel,which greatly improves t he efficiency of decomposition.At the same time,through the matching mechanism proposed in this paper,the decomposition results of each sub-tensor can be accurately merged into the p arameters of the hybrid model to be estimated.(2)Improved tensor decomposition algorithm.By studying and deducing the iteration for mula of traditional tensor decomposition algorithm,two operations of "setting negative value to zero"and "adding minimum positive value" are proposed,which not only ensure the non-n egative result of tensor decomposition,but also improve the robustness of the algorithm.(3)Design,implement and test the algorithm in Spark platform through Mapreduce mec hanism.By studying the idea of Mapreduce,the improved algorithm PTD is implemented in S park,which makes the algorithm have the ability to deal with large data.Experiments show that the improvement of this paper can improve the efficiency of tens or decomposition.It can decompose tensor more efficiently on the basis of guaranteeing the a ccuracy.At the same time,the implementation of Mapreduce algorithm makes the algorithm have the ability to deal with large data.