Contrastive Feature Induction for Efficient Structure Learning of Conditional Random Fields

Structure learning of Conditional Random Fields (CRFs) can be cast into L1-regularized optimization problems, which can be solved by efficient gradient-based optimization methods. However, optimizing a fully linked model may require inference on dense graphs which can be time prohibitive and inaccurate. Gain-based or gradient-based feature selection methods avoid this problem by starting from an empty model and incrementally adding top ranked features to it. However, training time with these incremental methods can be dominated by the cost of evaluating the gain or gradient of candidate features for high-dimensional problems. In this study we propose a fast feature evaluation algorithm called Contrastive Feature Induction (CFI) based on Mean Field Contrastive Divergence (CD MF ). CFI only evaluates a subset of features which involve variables with high signals (deviation from mean) or errors (prediction residue). We prove that the gradient of candidate features can be represented solely as a function of signals and errors, and that CFI is an efficient approximation of gradient-based evaluation methods. Experiments on synthetic and real datasets show competitive learning speed and accuracy of CFI on pairwise CRFs, compared to state-of-the-art structure learning methods such as full optimization over all features, and Grafting. More interestingly, CFI is not only faster than other methods but also produces models with higher prediction accuracy by focusing on large prediction errors during induction.