高维秩一非对称矩阵分解：球面情形
High-dimensional rank-one nonsymmetric matrix decomposition: the spherical case
摘要：
研究了加性高斯白噪声下秩1非对称矩阵的估计问题。估计的矩阵可以写成两个向量的外积，我们来看看两个向量均匀分布在球体上的特殊情况。我们证明了一个复制对称公式的平均互信息之间的这些向量和观察在高维制度。这超出了以前的结果，认为向量的独立和相同的分布元素。所使用的方法可以扩展到秩一张量问题。
英文摘要：
We consider the problem of estimating a rank-one nonsymmetric matrix under additive white Gaussian noise. The matrix to estimate can be written as the outer product of two vectors and we look at the special case in which both vectors are uniformly distributed on spheres. We prove a replica-symmetric formula for the average mutual information between these vectors and the observations in the high-dimensional regime. This goes beyond previous results which considered vectors with independent and identically distributed elements. The method used can be extended to rank-one tensor problems.
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