Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials

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Authors Mark W. Schmidt, Kevin P. Murphy
Journal/Conference Name AISTATS
Paper Category
Paper Abstract Previous work has examined structure learning in log-linear models with `1regularization, 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 `1-regularization with overlapping groups. 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 subroutine for solving the overlapping group `1regularization 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.
Date of publication 2010
Code Programming Language MATLAB

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