The Research On Gaussian Mean Field Algorithms

Graphical models are important methods for uncertain knowledge representation and reasoning in Artificial Intelligence. Since the complexities of exact inferences on graphical model are exponential, many approximate inferences, such as variational method, sampling method, loopy propagation, and qualitative method, have been developed, and the variational method has become the favourite of approximate inference community due to its sound theoretical foundation, low computational complexity, high convergence rate, and tight upper and lower bounds. Currently the majority of existing researches of variational inference method on graphical models concern with the methods, theories and properties from statistical points of view, and little attention has been paid to the basic algorithms and elementary properties in computational perspective.In this thesis, an algorithmic approach is adopted to variational inference on Gaussian Markov random field models. Following are the main results.First, a formal definition of graphical models is proposed, which represents the conditional independence and joint probabilistic distribution of random variables in an 8-tuple formalism. Second, the Gaussian exact variational inference algorithm and the Gaussian mean field variational inference algorithm are designed based on the Gaussian Markov random field models. Third, the elementary properties, such as convergence, accuracy and complexity, of the algorithms designed in this thesis are investigated. Finally, the theoretical results are demonstrated by numerical simulation experiments.