IMPACTS OF HIGH DIMENSIONALITY IN FINITE SAMPLES
IMPACTS OF HIGH DIMENSIONALITY IN FINITE SAMPLES
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DOI：
10.1214/13-aos1149
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发表时间：
2013-08-01
影响因子：
4.5
通讯作者：
Lv, Jinchi
中科院分区：
文献类型：
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作者：
Lv, Jinchi
高维数据集通常在科学研究的各个领域中出现的许多当代应用中收集。我们提出了两种观点的有限样本在高维：概率和非概率。从概率的观点出发，建立了椭圆分布下大型随机设计矩阵的集中性和鲁棒火花界，其中集中性与确定性屏蔽性有关，鲁棒火花界与稀疏模型可辨识性有关.揭示了一种有趣的高维浓度现象。从非概率的观点出发，我们在稀疏模型上得到了具有距离约束的维数的一般界。这些结果提供了新的见解，在有限的样本高维的影响。
High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one. With the probabilistic view, we establish the concentration property and robust spark bound for large random design matrix generated from elliptical distributions, with the former related to the sure screening property and the latter related to sparse model identifiability. An interesting concentration phenomenon in high dimensions is revealed. With the nonprobabilistic view, we derive general bounds on dimensionality with some distance constraint on sparse models. These results provide new insights into the impacts of high dimensionality in finite samples.