论文标题
矢量的宏观分析近似消息传递在模型不匹配设置中
Macroscopic Analysis of Vector Approximate Message Passing in a Model Mismatch Setting
论文作者
论文摘要
向量近似消息传递（VAMP）是用于广义线性模型的有效近似推理算法。尽管VAMP表现出色，尤其是当测量矩阵从旋转不变的合奏中采样时，现有的收敛性和性能分析主要受到正确的后验分布可用的情况。在这里，我们扩展了在推理阶段未使用正确后验分布的情况的分析。我们得出状态进化方程，从宏观上描述了鞋面的动力学，并表明它们的固定点与通过统计力学的复制方法获得的复制副本对称解决方案一致。我们还表明，鞋面的固定点可以表现出微观的不稳定性，其临界条件与破坏复制品对称性的临界条件一致。数值实验的结果支持我们的发现。
Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally invariant ensembles, existing convergence and performance analyses have been limited mostly to cases in which the correct posterior distribution is available. Here, we extend the analyses for cases in which the correct posterior distribution is not used in the inference stage. We derive state evolution equations, which macroscopically describe the dynamics of VAMP, and show that their fixed point is consistent with the replica symmetric solution obtained by the replica method of statistical mechanics. We also show that the fixed point of VAMP can exhibit a microscopic instability, the critical condition of which agrees with that for breaking the replica symmetry. The results of numerical experiments support our findings.
