Abstract
In this paper, we present a nonconvex alternating minimization optimization algorithm for low-rank and sparse structure pursuit. Compared with convex relaxation based methods, the proposed algorithm is computationally more efficient for large scale problems. In our study, we define a notion of bounded difference of gradients, based on which we rigorously prove that with suitable initialization, the proposed nonconvex optimization algorithm enjoys linear convergence to the global optima and exactly recovers the underlying low rank and sparse matrices under standard conditions such as incoherence and sparsity conditions. For a wide range of statistical models such as multi-task learning and robust principal component analysis (RPCA), our algorithm provides a principled approach to learning the low rank and sparse structures with provable guarantee. Thorough experiments on both synthetic and real datasets backup our theory.
Original language | English (US) |
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Pages | 600-609 |
Number of pages | 10 |
State | Published - Jan 1 2016 |
Event | 19th International Conference on Artificial Intelligence and Statistics, AISTATS 2016 - Cadiz, Spain Duration: May 9 2016 → May 11 2016 |
Conference
Conference | 19th International Conference on Artificial Intelligence and Statistics, AISTATS 2016 |
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Country/Territory | Spain |
City | Cadiz |
Period | 5/9/16 → 5/11/16 |
Funding
We would like to thank the anonymous reviewers for their helpful comments. Gu is supported by his startup funding at Department of Systems and Information Engineering, University of Virginia. Wang and Liu are partially supported by the grants NSF IIS1408910, NSF IIS1332109, NIH R01MH102339, NIH R01GM083084, and NIH R01HG06841.
ASJC Scopus subject areas
- Artificial Intelligence
- Statistics and Probability