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FMSPレクチャーズ
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 担当者 | 河野俊丈 |
|---|
2015年12月02日(水)
14:55-18:00 数理科学研究科棟(駒場) 056号室
"Learning theory and sparsity" 全3回講演の(2)
Arnak Dalalyan 氏 (ENSAE ParisTech)
(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
"Learning theory and sparsity" 全3回講演の(2)
Arnak Dalalyan 氏 (ENSAE ParisTech)
(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)
[ 講演概要 ]
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
[ 参考URL ]In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
