论文标题
高维级别一项非对称矩阵分解：球形案例
High-dimensional rank-one nonsymmetric matrix decomposition: the spherical case
论文作者
论文摘要
我们考虑在添加白色高斯噪声下估计一个排名一号的非对称矩阵的问题。估计矩阵可以写为两个向量的外产物，我们看一下两个向量在球上均匀分布的特殊情况。我们证明了这些向量之间平均互信息和高维度中的观察结果的复制对称公式。这超出了以前的结果，后者考虑了具有独立且分布相同的元素的向量。所使用的方法可以扩展到排名一张量的问题。
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.
