图 书 馆
含噪声和缺失数据的高维回归：非凸性的可证明保证High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity |
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| 课程网址: | http://videolectures.net/nips2011_loh_nonconvexity/ |
| 主讲教师: | Po-Ling Loh |
| 开课单位: | 加州大学 |
| 开课时间: | 2012-01-25 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependencies. We study these issues in the context of high-dimensional sparse linear regression, and propose novel estimators for the cases of noisy, missing, and/or dependent data. Many standard approaches to noisy or missing data, such as those using the EM algorithm, lead to optimization problems that are inherently non-convex, and it is difficult to establish theoretical guarantees on practical algorithms. While our approach also involves optimizing non-convex programs, we are able to both analyze the statistical error associated with any global optimum, and prove that a simple projected gradient descent algorithm will converge in polynomial time to a small neighborhood of the set of global minimizers. On the statistical side, we provide non-asymptotic bounds that hold with high probability for the cases of noisy, missing, and/or dependent data. On the computational side, we prove that under the same types of conditions required for statistical consistency, the projected gradient descent algorithm will converge at geometric rates to a near-global minimizer. We illustrate these theoretical predictions with simulations, showing agreement with the predicted scalings. |
| 关 键 词: | 高维回归; 数据预测 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-11-30：zyk |
| 最后编审: | 2020-11-30：zyk |
| 阅读次数: | 36 |