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# PAC-Bayesian Collective Stability

*Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics*, PMLR 33:585-594, 2014.

#### Abstract

Recent results have shown that the generalization error of structured predictors decreases with both the number of examples and the size of each example, provided the data distribution has weak dependence and the predictor exhibits a smoothness property called collective stability. These results use an especially strong definition of collective stability that must hold uniformly over all inputs and all hypotheses in the class. We investigate whether weaker definitions of collective stability suffice. Using the PAC-Bayes framework, which is particularly amenable to our new definitions, we prove that generalization is indeed possible when uniform collective stability happens with high probability over draws of predictors (and inputs). We then derive a generalization bound for a class of structured predictors with variably convex inference, which suggests a novel learning objective that optimizes collective stability.