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統計数学セミナー
過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
| 担当者 | 吉田朋広、荻原哲平、小池祐太 |
|---|---|
| セミナーURL | http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/ |
| 目的 | 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う. |
2015年12月03日(木)
16:40-18:00 数理科学研究科棟(駒場) 123号室
本講演は,数物フロンティア・リーディング大学院のFMSPレクチャーズとして行います．
Arnak Dalalyan 氏 (ENSAE ParisTech)
Learning theory and sparsity ～ Sparsity and low rank matrix learning ～
本講演は,数物フロンティア・リーディング大学院のFMSPレクチャーズとして行います．
Arnak Dalalyan 氏 (ENSAE ParisTech)
Learning theory and sparsity ～ Sparsity and low rank matrix learning ～
[ 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.
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.
