Approximate Message Passing Algorithms for Inference and Optimization

消息传递算法用于各种应用中的概率推理，包括通信、计算机视觉和机器学习。近年来，将这些算法的近似应用于稀疏回归和压缩感知等变量依赖图稠密的问题受到了广泛的关注。尽管在这些背景下取得了经验上的成功，但我们还没有对近似信息传递(AMP)有一个完善的理论理解。这个项目的目的是从理论上描述近似消息传递工作良好的条件。该项目还将研究AMP在新设置中的应用，例如实现容量的代码、稀疏近似和数据压缩。该项目涉及多个EPSRC研究领域，包括数字信号处理、射频和微波通信以及统计和应用概率。

Message-passing algorithms are used for probabilistic inference in a variety of applications including communications, computer vision, and machine learning. Recently, there has been much interest in applying approximations of these algorithms to problems such as sparse regression and compressed sensing, where the dependence graph of the variables is dense. Despite empirical success in these settings, we do not have a sound theoretical understanding of approximate message-passing (AMP) yet. This project aims to theoretically characterize conditions under which does approximate message-passing works well. The project will also investigate applications of AMP to new settings such as capacity-achieving codes, sparse approximation, and data compression. The project is relevant to multiple EPSRC research areas including, Digital signal processing, RF and microwave communications, and Statistics and Applied probability.