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An introduction to variational methods for graphical models. (English) Zbl 0945.68164

Summary: This paper presents a tutorial introduction to the use of variational methods for inference and learning in graphical models (Bayesian networks and Markov random fields). We present a number of examples of graphical models, including the QMR-DT database, the sigmoid belief network, the Boltzmann machine, and several variants of hidden Markov models, in which it is infeasible to run exact inference algorithms. We then introduce variational methods, which exploit laws of large numbers to transform the original graphical model into a simplified graphical model in which inference is efficient. Inference in the simplified model provides bounds on probabilities of interest in the original model. We describe a general framework for generating variational transformations based on convex duality. Finally, we return to the examples and demonstrate how variational algorithms can be formulated in each case.

MSC:

68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
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