Random linear mappings are widely used in modern signal processing, compressed sensing, and machine learning. These mappings may be used to embed the data into a significantly lower dimension while at the same time preserving useful information. This is done by approximately preserving the distances between data points, which are assumed to belong to . Thus, the performance of these mappings is usually captured by how close they are to an isometry on the data. Gaussian linear mappings have been the object of much study, while the sub-Gaussian settings is not yet fully understood. In the latter case, the performance depends on the sub-Gaussian norm of the rows. In many applications, e.g., compressed sensing, this norm may be large, or even growing with dimension, and thus it is important to characterize this dependence.

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集合上的亚高斯矩阵：最优尾依赖及其应用

随机线性映射广泛用于现代信号处理、压缩感知和机器学习。这些映射可用于将数据嵌入显着较低的维度，同时保留有用的信息。这是通过近似保留假设属于 的数据点之间的距离来完成的。因此，这些映射的性能通常通过它们与数据等距的接近程度来衡量。高斯线性映射一直是大量研究的对象，而亚高斯设置尚未完全理解。在后一种情况下，性能取决于行的亚高斯范数。在许多应用中，例如压缩感知，这个范数可能很大，甚至随着维度而增长，因此表征这种依赖性很重要。