We present a simple, yet useful result about the expected value of the determinant of random sum of rank-one matrices. Computing such expectations in general may involve a sum over exponentially many terms. Nevertheless, we show that an interesting and useful class of such expectations that arise in, e.g., D-optimal estimation and random graphs can be computed efficiently via computing a single determinant.

中文翻译：

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关于秩一矩阵随机和的行列式的期望值

我们提出了一个关于秩一矩阵随机和的行列式的期望值的简单但有用的结果。一般来说，计算这种期望可能涉及指数多个项的总和。然而，我们表明，可以通过计算单个行列式有效地计算出在例如 D 最优估计和随机图中出现的一类有趣且有用的此类期望。