Abstract

Structured learning is appropriate when predicting structured outputs such as trees, graphs, or sequences. Most prior work requires the training set to consist of complete trees, graphs or sequences. Specifying such detailed ground truth can be tedious or infeasible for large outputs. Our main contribution is a large margin formulation that makes structured learning from only partially annotated data possible. The resulting optimization problem is non-convex, yet can be efficiently solve by concave-convex procedure (CCCP) with novel speedup strategies. We apply our method to a challenging trackingby-assignment problem of a variable number of divisible objects. On this benchmark, using only 25% of a full annotation we achieve a performance comparable to a model learned with a full annotation. Finally, we offer a unifying perspective of previous work using the hinge, ramp, or max loss for structured learning, followed by an empirical comparison on their practical performance.