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On The Projection Operator to A Three-view Cardinality Constrained Set
Haichuan Yang · Shupeng Gui · Chuyang Ke · Daniel Stefankovic · Ryohei Fujimaki · Ji Liu

Tue Aug 08 01:30 AM -- 05:00 AM (PDT) @ Gallery #89

The cardinality constraint is an intrinsic way to restrict the solution structure in many domains, for example, sparse learning, feature selection, and compressed sensing. To solve a cardinality constrained problem, the key challenge is to solve the projection onto the cardinality constraint set, which is NP-hard in general when there exist multiple overlapped cardinality constraints. In this paper, we consider the scenario where the overlapped cardinality constraints satisfy a Three-view Cardinality Structure (TVCS), which reflects the natural restriction in many applications, such as identification of gene regulatory networks and task-worker assignment problem. We cast the projection into a linear programming, and show that for TVCS, the vertex solution of this linear programming is the solution for the original projection problem. We further prove that such solution can be found with the complexity proportional to the number of variables and constraints. We finally use synthetic experiments and two interesting applications in bioinformatics and crowdsourcing to validate the proposed TVCS model and method.

Author Information

Haichuan Yang (University of Rochester)
Shupeng Gui (University of Rochester)
Chuyang Ke (University of Rochester)
Daniel Stefankovic (University of Rochester)
Ryohei Fujimaki (-)
Ji Liu (University of Rochester)

Ji Liu is an Assistant Professor in Computer Science, Electrical and Computer Engineering, and Goergen Institute for Data Science at University of Rochester (UR). He received his Ph.D. in Computer Science from University of Wisconsin-Madison. His research interests focus on distributed optimization and machine learning. He also has rich experiences in various data analytics applications in healthcare, bioinformatics, social network, computer vision, etc. His recent research focus is on asynchronous parallel optimization, sparse learning (compressed sensing) theory and algorithm, structural model estimation, online learning, abnormal event detection, feature / pattern extraction, etc. He published more than 40 papers in top CS journals and conferences including JMLR, SIOPT, TPAMI, TIP, TKDD, NIPS, ICML, UAI, SIGKDD, ICCV, CVPR, ECCV, AAAI, IJCAI, ACM MM, etc. He won the award of Best Paper honorable mention at SIGKDD 2010 and the award of Best Student Paper award at UAI 2015.

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