论文标题
在消息传递算法中热情启动
Warm-Starting in Message Passing algorithms
论文作者
论文摘要
矢量近似消息传递（VAMP）提供了以贝叶斯最佳方式解决线性反问题的手段，假设测量算子足够随机。但是，vamp需要在每次迭代中实现线性最小平方误差（LMMSE）估计器，这使得算法对于大规模问题而棘手。在这项工作中，我们提出了一类温暖的（WS）方法，该方法在vamp中提供了LMMSE的可扩展近似。我们表明，配备了该类方法的消息传递（MP）算法可以收敛到鞋面的固定点，同时具有与AMP成正比的每视学计算复杂性。此外，我们还提供了使用一种WS方法的MP的Onsager校正和多维状态演变。最后，我们表明，最近提出的记忆放大器（MAMP）算法中使用的近似方法是开发类方法类别的特殊情况。
Vector Approximate Message Passing (VAMP) provides the means of solving a linear inverse problem in a Bayes-optimal way assuming the measurement operator is sufficiently random. However, VAMP requires implementing the linear minimum mean squared error (LMMSE) estimator at every iteration, which makes the algorithm intractable for large-scale problems. In this work, we present a class of warm-started (WS) methods that provides a scalable approximation of LMMSE within VAMP. We show that a Message Passing (MP) algorithm equipped with a method from this class can converge to the fixed point of VAMP while having a per-iteration computational complexity proportional to that of AMP. Additionally, we provide the Onsager correction and a multi-dimensional State Evolution for MP utilizing one of the WS methods. Lastly, we show that the approximation approach used in the recently proposed Memory AMP (MAMP) algorithm is a special case of the developed class of WS methods.
