Bethe Learning of Conditional Random Fields via MAP Decoding

Many machine learning tasks can be formulated in terms of predicting structured outputs. In frameworks such as the structured support vector machine (SVM-Struct) and the structured perceptron, discriminative functions are learned by iteratively applying efficient maximum a posteriori (MAP) decoding. However, maximum likelihood estimation (MLE) of probabilistic models over these same structured spaces requires computing partition functions, which is generally intractable. This paper presents a method for learning discrete exponential family models using the Bethe approximation to the MLE. Remarkably, this problem also reduces to iterative (MAP) decoding. This connection emerges by combining the Bethe approximation with a Frank-Wolfe (FW) algorithm on a convex dual objective which circumvents the intractable partition function. The result is a new single loop algorithm MLE-Struct, which is substantially more efficient than previous double-loop methods for approximate maximum likelihood estimation. Our algorithm outperforms existing methods in experiments involving image segmentation, matching problems from vision, and a new dataset of university roommate assignments.

Learning Soft Linear Constraints with Application to Citation Field Extraction

Accurately segmenting a citation string into fields for authors, titles, etc. is a challenging task because the output typically obeys various global constraints. Previous work has shown that modeling soft constraints, where the model is encouraged, but not require to obey the constraints, can substantially improve segmentation performance. On the other hand, for imposing hard constraints, dual decomposition is a popular technique for efficient prediction given existing algorithms for unconstrained inference. We extend the technique to perform prediction subject to soft constraints. Moreover, with a technique for performing inference given soft constraints, it is easy to automatically generate large families of constraints and learn their costs with a simple convex optimization problem during training. This allows us to obtain substantial gains in accuracy on a new, challenging citation extraction dataset.