Research On Multinomial Processing Tree Models And Its Applications

Multinomial Processing Tree Models (MPT) is an authoring statistical modeling and analysis method from the field of social science. Basically speaking, it is a method of using a tree-like structure to represent the original latent logical/information processes placed in each of different hierarchical stages on the basis of the current background disciplines and related theories, where the logic path selections of each information processes will now be considered as the form of a branch probability parameter. Thus, some certain statistical tools can be employed to perform quantitative analysis for every parameter-estimation computed by the observed categorical data, which can also be the foundation of conclusions. The first successful application of MPT modeling method is the modeling of latent cognitive processes in cognitive science, and then has been extended to a variety of paradigms of sociology, linguistic, logic, data mining and artificial intelligence. Comparing with other common modeling methods, it has clear advantages in the aspects of logic structure and conclusion generation. However, there are still some problems, such as the complex model expression as well as the slow convergence speed of model identification, which can be very obviously while handling a model with many sub-trees or independent parameters.On the basis of an intensive study of the related theories and algorithms of MPT models, this paper aims of enhancing the efficiencies of model expressions and algorithm. On the one hand, the encoding algorithms as well as the equivalent transformation rules of MPT models were proposed to compress the model information into one-dimensional space; on the other hand, two algorithms have been developed to speed up the original parameter estimation algorithm. Then MPT models have been extended to modeling and analyze contingence tables for mining specific associations, which have been acquiesced good effects. This paper includes these contents as follows:Firstly, the brief history and the current research and application processes of MPT models have been introduced, and then discussed and improved their basic theories and algorithm. The model characteristics as well as the standard modeling processes have been also represented, following with an applications and the comparison with another method.Secondly, combining the characteristics of the model structure and certain concepts of Data Structure, this paper investigated and developed the original encoding algorithm for content-free language, and established the framework of code expression of MPT models systematically by 1) the DLR-based encoding/decoding algorithms for Binary-MPT model which ensure the unique relationship between structure and strings; 2) the production-based trans-coding rules to perform model structures change according to order constrains within this framework; and 3) Encoding algorithm-based binarization of Multi-link MPT models, which ensured all the MPT models can be handled in the framework of content-free languages.Thirdly, on the purpose of handling the efficiency problem of the original identification algorithm for MPT models, this paper presented an approach that accelerates the convergence speed of the algorithm by 1) adjusting suitable initial positions for certain parameters to reduce required iterative times, and 2) using a series of operations between/among a set of matrices that are specific to the original model structure and information to reduce the time required for a single iteration. Compared with traditional algorithms, the simulation results showed the proposed algorithm had superior efficiency in interpreted languages as well as better algorithm readability and structure flexibility. In particular, these two algorithms were able to be combined to integrate their own advantages for improving the convergence speed significantly, which had been approved by a series of applications with different sizes.Fourthly, considering the shortage of some classic tools such as log-linear models, this paper proposed to use a MPT model as an alternative/additional method to investigate the contingence tables by 1) using combined branches in MPT tree-like structures with several additional parameters to perform personalized modeling for target table on the basis of standard structure of MPT models, and 2) latent class/group could be employed to classify categories according to characteristics of original tables for reducing the effect of the model hypothesis as well as performing analogy between them. Both of these two methods could provided higher Goodness-of-fit of MPT models for some complex contingency tables, and then could also be the foundations of latent relationship discovery as well as specific rule extraction. The comparison results between this modeling approach and other mainstream methods while solving some classic data as well as a latest investigation report shows MPT models can fit certain complex contingence tables and be able to generate valuable conclusions.Finally, the entire research has been summarized, following with the future direction discussions.