  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.
