Material Detail

This video was recorded at NIPS Workshop on Algebraic and Combinatorial Methods in Machine Learning, Whistler 2008. 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.

Disciplines:

• Mathematics and Statistics  / Mathematics  / Discrete Mathematics  / Graph Theory

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