Measuring Learnability in Structured Prediction using Factor Graph Complexity ∗

We present a general theoretical analysis of structured prediction. By introducing a new complexity measure that explicitly factors in the structure of the output space and the loss function, we are able to derive new learning guarantees for hypothesis sets with an arbitrary factor graph decomposition. To the best of our knowledge, these are both the most favorable and the most general guarantees for structured prediction (and multiclass classification) currently known. They are data-dependent and applicable to a broad family of losses.