Efficiently Searching for Frustrated Cycles in MAP Inference
This work addresses a bottleneck in graphical model inference for applications like computer vision and relational data, offering an incremental improvement over prior methods that were limited to short cycles.
The paper tackles the problem of large integrality gaps in MAP inference due to frustrated cycles by introducing a nearly linear time algorithm for finding the most frustrated cycles of arbitrary length, enabling exact solutions for relational classification and stereo vision problems.
Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large integrality gap, due to frustrated cycles. One way to tighten the relaxation is to introduce additional constraints that explicitly enforce cycle consistency. Earlier work showed that cluster-pursuit algorithms, which iteratively introduce cycle and other higherorder consistency constraints, allows one to exactly solve many hard inference problems. However, these algorithms explicitly enumerate a candidate set of clusters, limiting them to triplets or other short cycles. We solve the search problem for cycle constraints, giving a nearly linear time algorithm for finding the most frustrated cycle of arbitrary length. We show how to use this search algorithm together with the dual decomposition framework and clusterpursuit. The new algorithm exactly solves MAP inference problems arising from relational classification and stereo vision.