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Jun, 2016
对称秩一矩阵估计的互信息: 复制公式的证明
Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
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Jean Barbier, Mohamad Dia, Nicolas Macris, Florent Krzakala, Thibault Lesieur...
TL;DR
该论文研究如何采用严谨的方法证明低秩矩阵的对称秩一情况的互信息,进而表达最小均方误差和表征检测相位转变;同时介绍了一种被称为近似消息传递的迭代算法在贝叶斯最优条件下的优越性,并提出了通用的解决其他问题的方法。
Abstract
Factorizing
low-rank matrices
has many applications in machine learning and statistics. For probabilistic models in the
bayes optimal
setting, a general expression for the
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