In this paper,wegeneralize thebound propagation procedure toallowtheaddition of arbitrary cutting plane constraints, including those involving relaxed integer variables that do not appear in existing bound propagation formulations.

Semantic segmentation is a popular task in computer vision, which assigns pixel-wise semantic labels for given images. It has been widely utilized to facilitate downstream applications such as video surveillance and autonomous driving. Recent progress on image semantic segmentation has been drivenbydeep neural networks trained onalargeamount oflabeled data, which are yet expensive to obtain. An alternative way is to generate synthetic images with pixel-level ground truth readily available in an effortless way [1,2].

Via a sample-based learning mechanism, we prove the first guarantees on how much revenue can be preserved by truthfulmulti-item,multi-bidderauctions(forlimitedsupply)whenonlyarandom unknownfraction ofthepopulation participates inthemarket.

Conversely, the opposite scenario is relatively benign.