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Seminar on Probability and Statistics
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Organizer(s) | Nakahiro Yoshida, Teppei Ogihara, Yuta Koike |
|---|
2015/12/02
14:55-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～
[ Abstract ]
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.
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.
