图 书 馆
概率分布RKHS嵌入的核选择和可分类性Kernel Choice and Classifiability for RKHS Embeddings of Probability Distributions |
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| 课程网址: | http://videolectures.net/nips09_sriperumbudur_kcc/ |
| 主讲教师: | Bharath K.Sriperumbudur |
| 开课单位: | 加州大学 |
| 开课时间: | 2010-01-19 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Embeddings of probability measures into reproducing kernel Hilbert spaces have been proposed as a straightforward and practical means of representing and comparing probabilities. In particular, the distance between embeddings (the maximum mean discrepancy, or MMD) has several key advantages over many classical metrics on distributions, namely easy computability, fast convergence and low bias of finite sample estimates. An important requirement of the embedding RKHS is that it be characteristic: in this case, the MMD between two distributions is zero if and only if the distributions coincide. Three new results on the MMD are introduced in the present study. First, it is established that MMD corresponds to the optimal risk of a kernel classifier, thus forming a natural link between the distance between distributions and their ease of classification. An important consequence is that a kernel must be characteristic to guarantee classifiability between distributions in the RKHS. Second, the class of characteristic kernels is broadened to incorporate all bounded, continuous strictly positive definite kernels: these include non-translation invariant kernels and kernels on non-compact domains. Third, a generalization of the MMD is proposed for families of kernels, as the supremum over MMDs on a class of kernels (for instance the Gaussian kernels with different bandwidths). This extension is necessary to obtain a single distance measure if a large selection or class of characteristic kernels is potentially appropriate. This generalization is reasonable, given that it corresponds to the problem of learning the kernel by minimizing the risk of the corresponding kernel classifier. The generalized MMD is shown to have consistent finite sample estimates, and its performance is demonstrated on a homogeneity testing example. |
| 关 键 词: | 概率测度; 样本估计; 核分类器 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2023-03-14：chenjy |
| 最后编审: | 2023-03-14：chenjy |
| 阅读次数: | 42 |