Consistent Structured Estimation for Weighted Bipartite Matching

author: Tibério Caetano, National ICT Australia
author: James Petterson, National ICT Australia
author: Julian McAuley, Department of Computer Science and Engineering, UC San Diego
published: Dec. 20, 2008,   recorded: December 2008,   views: 321
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Description

Given a weighted bipartite graph, the assignment problem consists of finding the heaviest perfect match. This is a classical problem in combinatorial optimization, which is solvable exactly and efficiently by standard methods such as the Hungarian algorithm, and is widely applicable in real-world scenarios. We give an exponential family model for the assignment problem. Edge weights are obtained from a suitable composition of edge features and a parameter vector, which is learned so as to maximize the likelihood of a sample consisting of training graphs and their labeled matches. The resulting consistent estimator contrasts with existing max-margin structured estimators, which are inconsistent for this problem.

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