Perez-Cruz and Ghahramani 2007 Conditional graphical models

Citation

Conditional graphical models, Perez-Cruz & Ghahramani, 2007, in Predicting Structured Data. MIT Press, Cambridge, MA, USA, pp. 265-282..

Summary

The authors propose a generalization of CRF-like algorithms which allows any multi-class learning algorithm to be used on the cliques in the graph. The first half of the paper is a nice review of the many CRF-like algorithms that existed beforehand. They put all these algorithms into a unified mathematical framework, and show that the learning procedures are solving a convex optimization problem. They show that they can simplify this convex optimization problem. This simplification allows them to use any multi-class learning algorithm (like SVMs) on the cliques in the graph. In addition, the optimization problem during training is easier, and decoding is identical to normal CRFs.

Method

MAP training of Conditional Random Fields (CRFs) can be cast into the form:

$\mathbf {w} _{MAP}={\text{arg}}\max _{\mathbf {w} }\ p(\mathbf {w} |\mathbf {Y} ,\mathbf {X} )={\stackrel {\text{argmin}}{\mathbf {w} }}$

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