Optimizing Nondecomposable Loss Functions in Structured Prediction

We develop an algorithm for structured prediction with nondecomposable performance measures. The algorithm learns parameters of Markov Random Fields (MRFs) and can be applied to multivariate performance measures. Examples include performance measures such as $(F_{beta })$ score (natural language processing), intersection over union (object category segmentation), Precision/Recall at k (search engines), and ROC area (binary classifiers). We attack this optimization problem by approximating the loss function with a piecewise linear function. The loss augmented inference forms a Quadratic Program (QP), which we solve using LP relaxation. We apply this approach to two tasks: object class-specific segmentation and human action retrieval from videos. We show significant improvement over baseline approaches that either use simple loss functions or simple scoring functions on the PASCAL VOC and H3D Segmentation datasets, and a nursing home action recognition dataset.