document: Constrained optimization for validation-guided conditional random field learning Conditional random fields ( CRFs ) are a class of undirected graphical models which have been widely used for classifying and labeling sequence data . The training of CRFs is typically formulated as an unconstrained optimization problem that maximizes the conditional likelihood . However , maximum likelihood training is prone to overfitting . To address this issue , we propose a novel constrained nonlinear optimization formulation in which the prediction accuracy of cross-validation sets are included as constraints . Instead of requiring multiple passes of training , the constrained formulation allows the cross-validation be handled in one pass of constrained optimization . The new formulation is discontinuous , and classical Lagrangian based constraint handling methods are not applicable . A new constrained optimization algorithm based on the recently proposed extended saddle point theory is developed to learn the constrained CRF model . Experimental results on gene and stock-price prediction tasks show that the constrained formulation is able to significantly improve the generalization ability of CRF training .
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