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From Sets to Multisets: Provable Variational Inference for Probabilistic Integer Submodular Models
Aytunc Sahin · Yatao Bian · Joachim Buhmann · Andreas Krause

Thu Jul 16 02:00 PM -- 02:45 PM & Fri Jul 17 03:00 AM -- 03:45 AM (PDT) @ None #None

Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest, because this domain relates naturally to many practical problem settings, such as multilabel graph cut, budget allocation and revenue maximization with discrete assignments. In contrast, the use of these functions for probabilistic modeling has received surprisingly little attention so far. In this work, we firstly propose the Generalized Multilinear Extension, a continuous DR-submodular extension for integer submodular functions. We study central properties of this extension and formulate a new probabilistic model which is defined through integer submodular functions. Then, we introduce a block-coordinate ascent algorithm to perform approximate inference for this class of models and finally, we demonstrate its effectiveness and viability on several real-world social connection graph datasets with integer submodular objectives.

Author Information

Aytunc Sahin (ETH Zurich)
Yatao Bian (Tencent AI Lab)
Joachim Buhmann (ETH Zurich)
Andreas Krause (ETH Zurich)

Andreas Krause is a Professor of Computer Science at ETH Zurich, where he leads the Learning & Adaptive Systems Group. He also serves as Academic Co-Director of the Swiss Data Science Center. Before that he was an Assistant Professor of Computer Science at Caltech. He received his Ph.D. in Computer Science from Carnegie Mellon University (2008) and his Diplom in Computer Science and Mathematics from the Technical University of Munich, Germany (2004). He is a Microsoft Research Faculty Fellow and a Kavli Frontiers Fellow of the US National Academy of Sciences. He received ERC Starting Investigator and ERC Consolidator grants, the Deutscher Mustererkennungspreis, an NSF CAREER award, the Okawa Foundation Research Grant recognizing top young researchers in telecommunications as well as the ETH Golden Owl teaching award. His research on machine learning and adaptive systems has received awards at several premier conferences and journals, including the ACM SIGKDD Test of Time award 2019 and the ICML Test of Time award 2020. Andreas Krause served as Program Co-Chair for ICML 2018, and is regularly serving as Area Chair or Senior Program Committee member for ICML, NeurIPS, AAAI and IJCAI, and as Action Editor for the Journal of Machine Learning Research.

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