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# Part & Clamp: Efficient Structured Output Learning

*Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics*, PMLR 22:877-885, 2012.

#### Abstract

Discriminative training for general graphical models is a challenging task, due to the intractability of the partition function. We propose a computationally efficient approach to estimate the partition sum in a structured learning problem. The key idea is a lower bound of the partition sum that can be evaluated in a fixed number of message passing iterations. The bound makes use of a subset of the variables, a feedback vertex set, which allows us to decompose the graph into tractable parts. Furthermore, a tightening strategy for the bound is presented, which finds the states of the feedback vertex set that maximally increase the bound, and clamps them. Based on this lower bound we derive batch and online learning algorithms and demonstrate their effectiveness on a computer vision problem.