Exponential Family Graph Matching and Ranking
James Petterson, Tiberio Caetano, Julian McAuley and Jin Yu
In: NIPS 2009, 6-11 Dec 2009, Vancouver, Canada.
We present a method for learning max-weight matching predictors in bipartite graphs. The method consists of performing maximum a posteriori estimation in exponential families with sufﬁcient statistics that encode permutations and data features. Although inference is in general hard, we show that for one very relevant application–document ranking–exact inference is efﬁcient. For general model instances, an appropriate sampler is readily available. Contrary to existing max-margin matching models, our approach is statistically consistent and, in addition, experiments with increasing sample sizes indicate superior improvement
over such models. We apply the method to graph matching in computer vision as well as to a standard benchmark dataset for learning document ranking, in which we obtain state-of-the-art results, in particular improving on max-margin variants.
The drawback of this method with respect to max-margin alternatives is its run-time for large graphs, which is comparatively high.