图 书 馆
TCA:非高斯数据的高维主成分分析TCA: High Dimensional Principal Component Analysis for non-Gaussian Data |
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| 课程网址: | http://videolectures.net/nips2012_han_component_analysis/ |
| 主讲教师: | Fang Han |
| 开课单位: | 约翰霍普金斯大学 |
| 开课时间: | 2013-01-16 |
| 课程语种: | 英语 |
| 中文简介: |  我们提出了一种高维半参数尺度变量主成分分析，命名为TCA，利用椭圆分布族与主成分分析之间的自然联系。椭圆分布族包括许多众所周知的多变量分布，如多元t和逻辑，并且由Fang（2002）使用copula技术扩展到metaelliptical。在本文 中，我们将元椭圆分布族扩展到一个更大的族，称为transelliptical。我们证明了TCA可以在transelliptical分布族中获得接近最优的s（log d / n）^ {1/2}估计一致性率，即使分布非常重，有无限的二阶矩，没有密度和拥有任意连续的边际分布。还提供具有显式速率的特征选择结果。 TCA也在数值模拟和大规模库存数据中实施，以说明其经验性能。理论和实验都证实了TCA几乎可以免费获得模型灵活性，估计精度和鲁棒性。 |
| 课程简介: | We propose a high dimensional semiparametric scaleinvariant principle component analysis, named TCA, by utilize the natural connection between the elliptical distribution family and the principal component analysis. Elliptical distribution family includes many well-known multivariate distributions like multivariate t and logistic and it is extended to the metaelliptical by Fang (2002) using the copula techniques. In this paper we extend the meta-elliptical distribution family to a even larger family, called transelliptical. We prove that TCA can obtain a near-optimal s(log d/n)^{1/2} estimation consistency rate in the transelliptical distribution family, even if the distributions are very heavy-tailed, have infinite second moments, do not have densities and possess arbitrarily continuous marginal distributions. A feature selection result with explicit rate is also provided. TCA is also implemented in both numerical simulations and large-scale stock data to illustrate its empirical performance. Both theories and experiments confirm that TCA can achieve model flexibility, estimation accuracy and robustness at almost no cost. |
| 关 键 词: | 椭圆分布族; 高维半参数尺度; 主成分分析 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-09-06：lxf |
| 阅读次数: | 115 |