Bethe Projections for Non-Local Inference
It addresses the challenge of incorporating non-local statistics into inference for structured prediction tasks, offering a flexible method that is incremental over existing variational and constrained inference approaches.
The paper tackles the problem of learning complex, non-local inference objectives in structured prediction while maintaining tractable inference, achieving state-of-the-art results on handwriting recognition and scalable performance on tasks like citation extraction and bird migration modeling.
Many inference problems in structured prediction are naturally solved by augmenting a tractable dependency structure with complex, non-local auxiliary objectives. This includes the mean field family of variational inference algorithms, soft- or hard-constrained inference using Lagrangian relaxation or linear programming, collective graphical models, and forms of semi-supervised learning such as posterior regularization. We present a method to discriminatively learn broad families of inference objectives, capturing powerful non-local statistics of the latent variables, while maintaining tractable and provably fast inference using non-Euclidean projected gradient descent with a distance-generating function given by the Bethe entropy. We demonstrate the performance and flexibility of our method by (1) extracting structured citations from research papers by learning soft global constraints, (2) achieving state-of-the-art results on a widely-used handwriting recognition task using a novel learned non-convex inference procedure, and (3) providing a fast and highly scalable algorithm for the challenging problem of inference in a collective graphical model applied to bird migration.