Statistical estimation in high dimensions: Rigorous results for nonconvex optimization
Event details
| Date | 05.11.2015 |
| Hour | 17:15 › 18:00 |
| Speaker | Prof. Martin Wainwright, Berkeley University |
| Location | |
| Category | Conferences - Seminars |
The classical complexity barrier in continuous optimization is between convex (solvable in polynomial time) and nonconvex (intractable in the worst-case setting). However, many problems of interest are not constructed adversarially, but instead arise from probabilistic models of scientific phenomena. Can we provide rigorous guarantees for such random ensembles of nonconvex optimization problems?
In this talk, we survey various positive answers to this question, including optimal results for sparse regression with nonconvex penalties, and direct approaches to low-rank matrix recovery. All of these results involve natural weakenings of convexity that hold for various classes of nonconvex functions, thus shifting the barrier between tractable and intractable.
Biography :
Martin Wainwright joined the faculty at University of California at Berkeley in Fall 2004, and is currently a Professor with a joint appointment between the Department of Statistics and the Department of Electrical Engineering and Computer Sciences. He received his Bachelor's degree in Mathematics from University of Waterloo, Canada, and his Ph.D. degree in Electrical Engineering and Computer Science (EECS) from Massachusetts Institute of Technology (MIT), for which he was awarded the George M. Sprowls Prize from the MIT EECS department in 2002. He is interested in high-dimensional statistics, information theory and statistics, and statistical machine learning. He has received an Alfred P. Sloan Foundation Research Fellowship (2005), IEEE Best Paper Awards from the Signal Processing Society (2008) and Communications Society (2010); the Joint Paper Award from IEEE Information Theory and Communication Societies (2012); a Medallion Lecturer (2013) of the Institute for Mathematical Statistics; a Section Lecturer at the International Congress of Mathematicians (2014); and the COPSS Presidents' Award in Statistics (2014). He is currently serving as an Associate Editor for the Annals of Statistics, Journal of Machine Learning Research, Journal of the American Statistical Association, and Journal of Information and Inference.
In this talk, we survey various positive answers to this question, including optimal results for sparse regression with nonconvex penalties, and direct approaches to low-rank matrix recovery. All of these results involve natural weakenings of convexity that hold for various classes of nonconvex functions, thus shifting the barrier between tractable and intractable.
Biography :
Martin Wainwright joined the faculty at University of California at Berkeley in Fall 2004, and is currently a Professor with a joint appointment between the Department of Statistics and the Department of Electrical Engineering and Computer Sciences. He received his Bachelor's degree in Mathematics from University of Waterloo, Canada, and his Ph.D. degree in Electrical Engineering and Computer Science (EECS) from Massachusetts Institute of Technology (MIT), for which he was awarded the George M. Sprowls Prize from the MIT EECS department in 2002. He is interested in high-dimensional statistics, information theory and statistics, and statistical machine learning. He has received an Alfred P. Sloan Foundation Research Fellowship (2005), IEEE Best Paper Awards from the Signal Processing Society (2008) and Communications Society (2010); the Joint Paper Award from IEEE Information Theory and Communication Societies (2012); a Medallion Lecturer (2013) of the Institute for Mathematical Statistics; a Section Lecturer at the International Congress of Mathematicians (2014); and the COPSS Presidents' Award in Statistics (2014). He is currently serving as an Associate Editor for the Annals of Statistics, Journal of Machine Learning Research, Journal of the American Statistical Association, and Journal of Information and Inference.
Practical information
- General public
- Free
Organizer
- Prof. Victor Panaretos
Contact
- Marie Munoz