In structured prediction, target objects have rich internal structure which
does not factorize into independent components and violates common i.i.d.
assumptions. This challenge becomes apparent through the exponentially large
output space in applications such as image segmentation or scene graph
generation. We present a novel PAC-Bayesian risk bound for structured
prediction wherein the rate of generalization scales not only with the number
of structured examples but also with their size. The underlying assumption,
conforming to ongoing research on generative models, is that data are generated
by the Knothe-Rosenblatt rearrangement of a factorizing reference measure. This
allows to explicitly distill the structure between random output variables into
a Wasserstein dependency matrix. Our work makes a preliminary step towards
leveraging powerful generative models to establish generalization bounds for
discriminative downstream tasks in the challenging setting of structured
prediction.

在结构化预测中，我们提出了一种新的 PAC-Bayesian 风险界来处理非分离因素和违反 i.i.d. 假设的情况，并按照生成模型的研究，将数据生成为基于 Knothe-Rosenblatt 排序的因子参考测量，以显式提取随机输出变量之间的结构，从而为有挑战性的结构化预测下游任务建立归纳界限提供了初步步骤。