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FMSPレクチャーズ
過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
| 担当者 | 河野俊丈 |
|---|
2015年12月03日(木)
16:40-18:00 数理科学研究科棟(駒場) 123号室
"Learning theory and sparsity" 全3回講演の(3)
Arnak Dalalyan 氏 (ENSAE ParisTech)
(3)Sparsity and low rank matrix learning. (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
"Learning theory and sparsity" 全3回講演の(3)
Arnak Dalalyan 氏 (ENSAE ParisTech)
(3)Sparsity and low rank matrix learning. (ENGLISH)
[ 講演概要 ]
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
[ 参考URL ]In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
