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MILAN STUDENY - Institute of Information Theory and Automation of the ASCR

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Linear optimization approach to statistical learning graphical models
24 April 2012 from 4:00 PM to 5:00 PM
201 Thomas Bldg.
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At first, it will be explained how the statistical task of learning Bayesian networkstructure, which is a special graphical model of conditional independence structure, can be transformed to a linear optimization task to maximize a certain linear function (determined by data) over a special integral polytope. Then suitable linear transformation of the optimization problem will be described, which allows to consider a polytope with zero-one vectors as vertices. Finally, by means of the concept of LP relaxation of the polytope, the transformed optimization task will be re-formulated in the form an integer programming problem, which seems to offer the way to solve the optimization task in practice. The talk is based on joint research with Raymond Hemmecke, Silvia Lindner (both TU Munich) and David Haws (U. of Kentucky).


[1] M. Studen´y, Probabilistic Conditional Independence Structures, Springer Verlag, 2005.

[2] M. Studen´y, J. Vomlel, R. Hemmecke, A geometric view on learning Bayesian network structures, International Journal of Approximate Reasoning 51 (2010) 578-586.

[3] M. Studen´y, D. Haws, R. Hemmecke, S. Lindner, Polyhedral approach to statistical learning graphical models, to appear in Proceedings of the 2nd CREST–SBM International Conference Harmony of Gr¨obner Bases and the Modern Industrial Society, World Scientific, 346-372.

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