An Introduction to Variational Methods for Graphical Models Export

@article{citeulike:162870, abstract = {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 simpified 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.}, address = {Hingham, MA, USA}, author = {Jordan, Michael I. and Ghahramani, Zoubin and Jaakkola, Tommi S. and Saul, Lawrence K.}, citeulike-article-id = {162870}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=339248.339252}, citeulike-linkout-1 = {http://dx.doi.org/10.1023/A:1007665907178}, day = {1}, doi = {10.1023/A:1007665907178}, issn = {08856125}, journal = {Machine Learning}, keywords = {gaussian, network, reviews, statistic, variational}, month = {November}, number = {2}, pages = {183--233}, posted-at = {2006-06-06 17:48:10}, priority = {2}, publisher = {Kluwer Academic Publishers}, title = {An Introduction to Variational Methods for Graphical Models}, url = {http://dx.doi.org/10.1023/A:1007665907178}, volume = {37}, year = {1999} }

TY - JOUR ID - citeulike:162870 L3 - citeulike-article-id:162870 N2 - 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 simpified 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. IS - 2 JF - Machine Learning SN - 08856125 AD - Hingham, MA, USA EP - 233 TI - An Introduction to Variational Methods for Graphical Models PB - Kluwer Academic Publishers VL - 37 SP - 183 KW - gaussian KW - network KW - reviews KW - statistic KW - variational AU - Jordan, Michael AU - Ghahramani, Zoubin AU - Jaakkola, Tommi AU - Saul, Lawrence PY - 1999/11/01/ UR - http://dx.doi.org/10.1023/A:1007665907178 ER -