  For joint inference over multiple variables, a variety of structured
prediction techniques have been developed to model correlations among variables
and thereby improve predictions. However, many classical approaches suffer from
one of two primary drawbacks: they either lack the ability to model high-order
correlations among variables while maintaining computationally tractable
inference, or they do not allow to explicitly model known correlations. To
address this shortcoming, we introduce `Graph Structured Prediction Energy
Networks,' for which we develop inference techniques that allow to both model
explicit local and implicit higher-order correlations while maintaining
tractability of inference. We apply the proposed method to tasks from the
natural language processing and computer vision domain and demonstrate its
general utility.
