在实践中,尽管非模块损失(Jaccard loss)已经被应用到结构化预测的设置中,但模块化损失(如Hamming loss)通常被应用来保持可牵引性。在本文中表明,Jaccard loss事实是一个子模损失,我们提出的凸代理提供了一个多项式时间的紧的上界。 在多分类问题背景下已经考虑过非模块的损失。使用模块化的Hamming loss和0-1子集损...
We propose instead a novel convex surrogate loss function for submodular losses, the Lovasz hinge, which leads to O(p log p) complexity with O(p) oracle accesses to the loss function to compute a gradient or cutting-plane. As a result, we have developed the first tractable convex ...