Towards Sharper Generalization Bounds for Structured Prediction

In this paper, we investigate the generalization performance of structured prediction learning and obtain state-of-the-art generalization bounds. Our analysis is based on factor graph decomposition of structured prediction algorithms, and we present novel margin guarantees from three different perspectives: Lipschitz continuity, smoothness, and space capacity condition. In the Lipschitz continuity scenario, we improve the square-root dependency on the label set cardinality of existing bounds to a logarithmic dependence. In the smoothness scenario, we provide generalization bounds that are not only a logarithmic dependency on the label set cardinality but a faster convergence rate of order O( 1 n ) on the sample size n. In the space capacity scenario, we obtain bounds that do not depend on the label set cardinality and have faster convergence rates than O( 1 √ n ). In each scenario, applications are provided to suggest that these conditions are easy to be satisfied.