The Lov\'asz Hinge: A Novel Convex Surrogate for Submodular Losses

Learning with non-modular losses is an important problem when sets of predictions are made simultaneously. The main tools for constructing convex surrogate loss functions for set prediction are margin rescaling and slack rescaling. In this work, we show that these strategies lead to tight convex surrogates iff the underlying loss function is increasing in the number of incorrect predictions. However, gradient or cutting-plane computation for these functions is NP-hard for non-supermodular loss functions. We propose instead a novel surrogate loss function for submodular losses, the Lov\'asz 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. We prove that the Lov\'asz hinge is convex and yields an extension. As a result, we have developed the first tractable convex surrogates in the literature for submodular losses. We demonstrate the utility of this novel convex surrogate through several set prediction tasks, including on the PASCAL VOC and Microsoft COCO datasets

The Emerging Trends of Multi-Label Learning

Exabytes of data are generated daily by humans, leading to the growing need for new efforts in dealing with the grand challenges for multi-label learning brought by big data. For example, extreme multi-label classification is an active and rapidly growing research area that deals with classification tasks with an extremely large number of classes or labels; utilizing massive data with limited supervision to build a multi-label classification model becomes valuable for practical applications, etc. Besides these, there are tremendous efforts on how to harvest the strong learning capability of deep learning to better capture the label dependencies in multi-label learning, which is the key for deep learning to address real-world classification tasks. However, it is noted that there has been a lack of systemic studies that focus explicitly on analyzing the emerging trends and new challenges of multi-label learning in the era of big data. It is imperative to call for a comprehensive survey to fulfill this mission and delineate future research directions and new applications.Comment: Accepted to TPAMI 202