图 书 馆
具有指数族噪声的低秩矩阵补全Low Rank Matrix Completion with Exponential Family Noise |
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| 课程网址: | https://videolectures.net/videos/colt2015_lafond_family_noise |
| 主讲教师: | Jean Lafond |
| 开课单位: | 信息不详。欢迎您在右侧留言补充。 |
| 开课时间: | 2025-02-04 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | The matrix completion problem consists in reconstructing a matrix from a sample of entries observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data fitting term and a nuclear norm penalization. Here, we investigate the case where the noise distribution belongs to the exponential family, is sub-exponential and consider a general sampling scheme. We first consider an estimator defined as the minimizer of the sum of a log-likelihood term and a nuclear norm penalization and prove an upper bound on the Frobenius prediction risk. The rate obtained improves on previous works on exponential family completion. When the sampling distribution is known, we propose a second estimator and prove an oracle inequality on the Kullback-Leibler divergence risk, which translates immediatly into an upper bound on the Frobenius risk. Finally, we show that all the rates obtained are minimax optimal up to a logarithmic factor. |
| 关 键 词: | 矩阵补全问题：核范数惩罚估计器：噪声分布 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2025-03-28：zsp |
| 最后编审: | 2025-03-28：zsp |
| 阅读次数: | 4 |