基于倾斜期望最大化的自适应得分向量近似消息传递：自调整超参数
Factor-Wise Parameter Learning in Score-Based VAMP
- Department of Computer Science, Nagoya Institute of Technology（名古屋工业大学计算机系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究针对近似消息传递方法中模块参数依赖正确设定的问题，开发自适应SC-VAMP，通过局部倾斜EM步骤更新参数，在特定假设和条件下形成贝叶斯最优不动点，线性和一位伯努利 - 高斯压缩感知数值结果显示能从不匹配初始化恢复近最优性能。
AI中文摘要：
近似消息传递方法为高维逆问题提供快速贝叶斯推理，但其性能和状态演化预测依赖于正确设定的模块参数。本文开发了基于得分的向量近似消息传递（SC-VAMP）的自适应版本。每个参数化因子通过局部倾斜期望最大化（EM）步骤更新，该步骤重用单输入单输出模块接口已计算的倾斜矩。在标准大系统状态演化假设和可识别条件下，匹配参数形成自适应递归的贝叶斯最优总体不动点。分别针对先验模块和似然/LMMSE模块进行论证，后者使用VAMP变换误差模型诱导的高斯腔。线性和一位伯努利 - 高斯压缩感知的数值结果表明，所提出的更新从严重不匹配的初始化中恢复了接近最优的性能。
英文摘要：
Score-based vector approximate message passing (SC-VAMP) builds state-evolution-predictable inference from modular soft-input soft-output (SISO) factors, but every factor must be handed correct parameters: a wrong sparsity rate, signal variance, or noise level distorts the tilted distributions and Onsager terms, raises the fixed-point mean-squared error (MSE), and invalidates matched state-evolution (SE) prediction. We let each factor learn its own parameters instead. An expectation-maximization (EM) M-step taken under the module's tilted distribution is attached to every parameterized factor and costs O(N) per module, because that distribution and its moments are precisely what the SISO rule already computes on the way to the score; the score-based interface and the Onsager correction are left untouched. Under standard large-system SE assumptions and identifiability conditions, the true parameters and the matched SE variance form a fixed point of the recursion, at which the estimate attains the replica minimum MSE (MMSE); prior factors and likelihood/linear-MMSE (LMMSE) factors are treated separately, the latter under the Gaussian cavity induced by the VAMP transformed-error model. On linear and one-bit Bernoulli-Gaussian compressed sensing, the updates recover near-oracle accuracy from strongly mismatched initializations.
