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Safe Element Screening for Submodular Function Minimization
Weizhong Zhang · Bin Hong · Lin Ma · Wei Liu · Tong Zhang

Wed Jul 11 09:15 AM -- 12:00 PM (PDT) @ Hall B #161

Submodular functions are discrete analogs of convex functions, which have applications in various fields, including machine learning and computer vision. However, in large-scale applications, solving Submodular Function Minimization (SFM) problems remains challenging. In this paper, we make the first attempt to extend the emerging technique named screening in large-scale sparse learning to SFM for accelerating its optimization process. We first conduct a careful studying of the relationships between SFM and the corresponding convex proximal problems, as well as the accurate primal optimum estimation of the proximal problems. Relying on this study, we subsequently propose a novel safe screening method to quickly identify the elements guaranteed to be included (we refer to them as active) or excluded (inactive) in the final optimal solution of SFM during the optimization process. By removing the inactive elements and fixing the active ones, the problem size can be dramatically reduced, leading to great savings in the computational cost without sacrificing any accuracy. To the best of our knowledge, the proposed method is the first screening method in the fields of SFM and even combinatorial optimization, thus pointing out a new direction for accelerating SFM algorithms. Experiment results on both synthetic and real datasets demonstrate the significant speedups gained by our approach.

Author Information

Weizhong Zhang (Tencent AI Lab)
Bin Hong (Zhejiang University)
Lin Ma (Tencent AI Lab)
Wei Liu (Tencent AI Lab)
Tong Zhang (Tecent AI Lab)
Tong Zhang

Tong Zhang is a professor of Computer Science and Mathematics at the Hong Kong University of Science and Technology. His research interests are machine learning, big data and their applications. He obtained a BA in Mathematics and Computer Science from Cornell University, and a PhD in Computer Science from Stanford University. Before joining HKUST, Tong Zhang was a professor at Rutgers University, and worked previously at IBM, Yahoo as research scientists, Baidu as the director of Big Data Lab, and Tencent as the founding director of AI Lab. Tong Zhang was an ASA fellow and IMS fellow, and has served as the chair or area-chair in major machine learning conferences such as NIPS, ICML, and COLT, and has served as associate editors in top machine learning journals such as PAMI, JMLR, and Machine Learning Journal.

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