论文标题
足够的统计记忆近似消息传递
Sufficient Statistic Memory Approximate Message Passing
论文作者
论文摘要
近似消息传递（AMP）类型算法已被广泛用于某些大型随机线性系统的信号重建。 AMP型算法的关键特征是可以通过状态进化正确描述它们的动力学。但是，状态进化不一定保证迭代算法的收敛性。为了解决原则上AMP类型算法的收敛问题，本文提出了在足够的统计条件下的记忆AMP（MAMP），称为足够的统计MAMP（SS-MAMP）。我们表明，SS-MAMP的协方差矩阵是L带和收敛的。给定任意乳房，我们可以通过阻尼来构建SS-MAMP，这不仅可以确保收敛性，而且可以保留正交性，即可以通过状态进化正确描述其动力学。
Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state evolution. However, state evolution does not necessarily guarantee the convergence of iterative algorithms. To solve the convergence problem of AMP-type algorithms in principle, this paper proposes a memory AMP (MAMP) under a sufficient statistic condition, named sufficient statistic MAMP (SS-MAMP). We show that the covariance matrices of SS-MAMP are L-banded and convergent. Given an arbitrary MAMP, we can construct the SS-MAMP by damping, which not only ensures the convergence, but also preserves the orthogonality, i.e., its dynamics can be correctly described by state evolution.
