图 书 馆
概率分布的几何推理Geometric Inference for Probability Distribution |
|
| 课程网址: | http://videolectures.net/mlss09us_chazal_gipd/ |
| 主讲教师: | Frederic Chazal |
| 开课单位: | 法国国家信息与自动化研究所 |
| 开课时间: | 2009-07-30 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Data often comes in the form of a point cloud sampled from an unknown compact subset of Euclidean space. The general goal of geometric inference is then to recover geometric and topological features (Betti numbers, curvatures,...) of this subset from the approximating point cloud data. In recent years, it appeared that the study of distance functions allows to address many of these questions successfully. However, one of the main limitations of this framework is that it does not cope well with outliers nor with background noise. In this talk, we will show how to extend the framework of distance functions to overcome this problem. Replacing compact subsets by measures, we will introduce a notion of distance function to a probability distribution. These functions share many properties with classical distance functions, which makes them suitable for inference purposes. In particular, by considering appropriate level sets of these distance functions, it is possible to associate in a robust way topological and geometric features to a probability measure. If time permits, we will also mention a few other potential applications of this framework. |
| 关 键 词: | 欧氏空间; 拓扑特征; 距离函数; 概率分布; 异常值 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2020-06-01：wuyq |
| 阅读次数: | 39 |