论文标题
矩阵二次形式的期望值，带有wishart分布式随机矩阵
Expected Value of Matrix Quadratic Forms with Wishart distributed Random Matrices
论文作者
论文摘要
为了探索随机梯度方法的限制，考虑一个由无限数量的二次函数组成的示例可能很有用。在这种情况下，确定随机噪声的期望值和协方差矩阵，即从有限样本产生的真实梯度和近似梯度的差异。指定协方差矩阵时，需要二次形式的QBQ的预期值，其中Q是一个愿望分布的随机矩阵，B是任意的固定对称矩阵。在得出E（QBQ）表达并考虑一些特殊情况后，使用数值示例来显示这些结果如何支持两种随机方法的比较。
To explore the limits of a stochastic gradient method, it may be useful to consider an example consisting of an infinite number of quadratic functions. In this context, it is appropriate to determine the expected value and the covariance matrix of the stochastic noise, i.e. the difference of the true gradient and the approximated gradient generated from a finite sample. When specifying the covariance matrix, the expected value of a quadratic form QBQ is needed, where Q is a Wishart distributed random matrix and B is an arbitrary fixed symmetric matrix. After deriving an expression for E(QBQ) and considering some special cases, a numerical example is used to show how these results can support the comparison of two stochastic methods.
