Tail inequalities for sums of random matrices that depend on the intrinsic dimension
Tail inequalities for sums of random matrices that depend on the intrinsic dimension
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DOI：
10.1214/ecp.v17-1869
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发表时间：
2012-12
影响因子：
0.5
通讯作者：
Daniel J. Hsu;S. Kakade;Tong Zhang
中科院分区：
文献类型：
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作者：
Daniel J. Hsu;S. Kakade;Tong Zhang
这项工作提供了指数尾不等式的随机矩阵，只依赖于内在的尺寸，而不是显式的矩阵尺寸的总和。这些尾部不等式类似于矩阵形式的Bauffff界和伯恩斯坦不等式，除了用一个迹量代替显式矩阵维数，即使显式维数很大或无穷大，迹量也可以很小。给出了协方差估计和近似矩阵乘法的一些应用以说明新界的实用性。
This work provides exponential tail inequalities for sums of random matrices that depend only on intrinsic dimensions rather than explicit matrix dimensions. These tail inequalities are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the explicit dimensions are large or infinite. Some applications to covariance estimation and approximate matrix multiplication are given to illustrate the utility of the new bounds.