Gradient Boosting for Conditional Random Fields
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In this paper, we present a gradient boosting algorithm for tree-shaped conditional random fields CRF. Conditional random fields are an important class of models for accurate structured prediction, but effective design of the feature functions is a major challenge when applying CRF models to real world data. Gradient boosting, which can induce and select functions, is a natural candidate solution for the problem. However, it is non-trivial to derive gradient boosting algorithms for CRFs, due to the dense Hessian matrices introduced by variable dependencies. We address this challenge by deriving a Markov Chain mixing rate bound to quantify the dependencies, and introduce a gradient boosting algorithm that iteratively optimizes an adaptive upper bound of the objective function. The resulting algorithm induces and selects features for CRFs via functional space optimization, with provable convergence guarantees. Experimental results on three real world datasets demonstrate that the mixing rate based upper bound is effective for training CRFs with non-linear potentials.