图 书 馆
对低秩核矩阵近似的分析Sharp analysis of low-rank kernel matrix approximation |
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| 课程网址: | http://videolectures.net/colt2013_bach_matrix/ |
| 主讲教师: | Francis R. Bach |
| 开课单位: | 水产养殖自然研究所 |
| 开课时间: | 2011-08-02 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces, a common practical limiting difficulty is the necessity of computing the kernel matrix, which most frequently leads to algorithms with running time at least quadratic in the number of observations n, i.e., O(n2). Low-rank approximations of the kernel matrix are often considered as they allow the reduction of running time complexities to O(p2n), where p is the rank of the approximation. The practicality of such methods thus depends on the required rank p. In this paper, we show that for approximations based on a random subset of columns of the original kernel matrix, the rank p may be chosen to be linear in the degrees of freedom associated with the problem, a quantity which is classically used in the statistical analysis of such methods, and is often seen as the implicit number of parameters of non-parametric estimators. This result enables simple algorithms that have sub-quadratic running time complexity, but provably exhibit the same predictive performance than existing algorithms, for any given problem instance, and not only for worst-case situations. |
| 关 键 词: | 核岭回归; 核逻辑; 正定核框架; 无穷维特征空间; 核矩阵; 原始内核; 隐式参数 |
| 课程来源: | 视频讲座网公开课 |
| 最后编审: | 2019-05-26：cwx |
| 阅读次数: | 88 |