图 书 馆
流形值狄利克雷过程Manifold-valued Dirichlet Processes |
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| 课程网址: | http://videolectures.net/icml2015_kim_dirichlet_processes/ |
| 主讲教师: | Hyunwoo J. Kim |
| 开课单位: | 威斯康星大学 |
| 开课时间: | 2015-12-05 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Statistical models for manifold-valued data permit capturing the intrinsic nature of the curved spaces in which the data lie and have been a topic of research for several decades. Typically, these formulations use geodesic curves and distances defined locally for most cases – this makes it hard to design parametric models globally on smooth manifolds. Thus, most (manifold specific) parametric models available today assume that the data lie in a small neighborhood on the manifold. To address this ‘locality’ problem, we propose a novel nonparametric model which unifies multivariate general linear models (MGLMs) using multiple tangent spaces. Our framework generalizes existing work on (both Euclidean and non-Euclidean) general linear models providing a recipe to globally extend the locally-defined parametric models (using a mixture of local models). By grouping observations into sub-populations at multiple tangent spaces, our method provides insights into the hidden structure (geodesic relationships) in the data. This yields a framework to group observations and discover geodesic relationships between covariates X and manifold-valued responses Y, which we call Dirichlet process mixtures of multivariate general linear models (DP-MGLM) on Riemannian manifolds. Finally, we present proof of concept experiments to validate our model. |
| 关 键 词: | 统计模型; 流行值数据; 黎曼流形 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2022-11-01：chenjy |
| 最后编审: | 2022-11-01：chenjy |
| 阅读次数: | 37 |