Research And Implementation Of Exact Inference On Discrete Dynamic Bayesian Network

Bayesian Networks is one of the methods of modeling the uncertainty problems. The high quality of which to model reality, simple representation and tractable computation make the model used widely. Dynamic Bayesian Networks is the development of Bayesian Networks, which is mainly used in modeling time series and sequential data. Hidden Markov Models and Kalman Filter Model which are the particular cases of Dynamic Bayesian Network have been used for speech recognition, bio-sequence analysis and tracking object. But for more generally Dynamic Bayesian Network, because of the diversity of representation and the complexity of the inference and learning process, there is no large-scale application in industry.In this paper, we start from basic theory of Bayesian network, explained the reason why it can model the reality. Three main tasks of Dynamic Bayesian Networks are mentioned respectively: The representation, inference and learning of the model.HMM, FHMM, CHMM, HHMM and AHMM- the five different representation forms are listed respectively, each of them has given a specific domain application.The inference of Dynamic Bayesian Network defines that the process of computing the probability of a query variable as a set of observed variables were given. This paper analyzed the inference algorithm on the discrete dynamic Bayesian network deeply, made a study of interface algorithm on general dynamic Bayesian network which of theory is based on the variable elimination, the junction tree algorithm on static Bayesian network and the forward-backward algorithm on HMM.After that, the maximum likelihood estimation and expectation maximization algorithm on Bayesian network are interpreted.At the last, a computing library named as libdbn is implemented based on the previous theoretical work, which can represents and do inference to Bayesian network. libdbn is comprised of the low level which implements by C++ and the high level which implements by Python. The most of algorithms in this paper have accomplished in it, so it can be used as a tool to model and inference the Bayesian Network, furthermore, it brings a new sight to researchers who would like to study deeply or to improve the implementation.