Variational methods for inference and estimation in graphical models
Graphical models enhance the representational power of probability models through qualitative characterization of their properties. This also leads to greater efficiency in terms of the computational algorithms that empower such representations. The increasing complexity of these models, however, quickly renders exact probabilistic calculations infeasible. We propose a principled framework for approximating graphical models based on variational methods. 
We develop variational techniques from the perspective that unifies and expands their applicability to graphical models. These methods allow the (recursive) computation of upper and lower bounds on the quantities of interest. Such bounds yield considerably more information than mere approximations and provide an inherent error metric for tailoring the approximations individually to the cases considered. These desirable properties, concomitant to the variational methods, are unlikely to arise as a result of other deterministic or stochastic approximations. 
The thesis consists of the development of this variational methodology for probabilistic inference, Bayesian estimation, and towards efficient diagnostic reasoning in the domain of internal medicine. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)