Convex structure learning in log-linear models beyond pairwise potentials

author: Mark Schmidt, Department of Computer Science, University of British Columbia
published: June 3, 2010,   recorded: May 2010,   views: 5907


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Previous work has examined structure learning in log-linear models with L1-regularization, largely focusing on the case of pairwise potentials. In this work we consider the case of models with potentials of arbitrary order, but that satisfy a hierarchical constraint. We enforce the hierarchical constraint using group L1-regularization with overlapping groups, and an active set method that enforces hierarchical inclusion allows us to tractably consider the exponential number of higher-order potentials. We use a spectral projected gradient method as a sub-routine for solving the overlapping group L1-regularization problem, and make use of a sparse version of Dykstra's algorithm to compute the projection. Our experiments indicate that this model gives equal or better test set likelihood compared to previous models.

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