论文标题
高维多层广义线性模型的估计 - 第二部分：ML-GAMP估计器
Estimation for High-Dimensional Multi-Layer Generalized Linear Model -- Part II: The ML-GAMP Estimator
论文作者
论文摘要
这是针对大型系统限制的多层广义线性模型（ML-GLM）的估计的两部分工作的第二部分。在第一部分中，我们分析了精确的MMSE估计器的渐近性能，并获得了一组可以表征其MSE性能的耦合方程。为了解决确切估计器的实现难度，本文继续提出近似解决方案ML-GAMP，可以通过将矩匹配的投影融合到高斯近似循环信念传播中来得出。然后，显示ML-GAMP估计器在其实现中具有极大的简单性，在该实现中，其触觉复杂性与GAMP一样低。对其渐近性能的进一步分析还表明，在大型系统限制中，其动力学MSE行为完全以一组简单的一维迭代方程为特征，称为状态进化（SE）。有趣的是，ML-GAMP的SE SE与精确的MMSE估计值完全相同的固定点，其固定点是通过复制品分析在I部分获得的。鉴于确切实现的贝叶斯优越性，该提出的估计器（如果融合）在MSE意义上是最佳的。
This is Part II of a two-part work on the estimation for a multi-layer generalized linear model (ML-GLM) in large system limits. In Part I, we had analyzed the asymptotic performance of an exact MMSE estimator, and obtained a set of coupled equations that could characterize its MSE performance. To work around the implementation difficulty of the exact estimator, this paper continues to propose an approximate solution, ML-GAMP, which could be derived by blending a moment-matching projection into the Gaussian approximated loopy belief propagation. The ML-GAMP estimator is then shown to enjoy a great simplicity in its implementation, where its per-iteration complexity is as low as GAMP. Further analysis on its asymptotic performance also reveals that, in large system limits, its dynamical MSE behavior is fully characterized by a set of simple one-dimensional iterating equations, termed state evolution (SE). Interestingly, this SE of ML-GAMP share exactly the same fixed points with an exact MMSE estimator whose fixed points were obtained in Part I via a replica analysis. Given the Bayes-optimality of the exact implementation, this proposed estimator (if converged) is optimal in the MSE sense.
