论文标题
方便的尾部边界，用于随机张量的总和
Convenient tail bounds for sums of random tensors
论文作者
论文摘要
这项工作为随机，独立，遗传张量的总和准备了新的概率范围。这些概率界限表征了随机张量总和的极端特征值的大型探索行为。我们将Lapalace Transform方法和Lieb的凹陷定理从矩阵扩展到张量，并应用这些工具来概括与名称Chernoff，Bennett和Bernstein相关的经典界限，从标量到张量设置。随机矩形张量总和的标准的尾巴边界也源自随机的Hermitian Tensors病例的推论。证明机制也可以应用于张量值的martingales和基于张量的Azuma，Hoeffding和McDiarmid的不平等现象。
This work prepares new probability bounds for sums of random, independent, Hermitian tensors. These probability bounds characterize large-deviation behavior of the extreme eigenvalue of the sums of random tensors. We extend Lapalace transform method and Lieb's concavity theorem from matrices to tensors, and apply these tools to generalize the classical bounds associated with the names Chernoff, Bennett, and Bernstein from the scalar to the tensor setting. Tail bounds for the norm of a sum of random rectangular tensors are also derived from corollaries of random Hermitian tensors cases. The proof mechanism can also be applied to tensor-valued martingales and tensor-based Azuma, Hoeffding and McDiarmid inequalities are established.
