Theoretical performance limits for message passing algorithms

消息传递算法是低复杂度算法，可在纠错和有损压缩等各种应用中实现最先进的经验性能。然而，它们在许多此类应用中缺乏理论性能保证。该项目将通过开发严格的密度演化方程来分析消息算法的性能。我们将从有损压缩问题开始，然后将该技术扩展到其他近似和推理问题。该项目直接涉及几个 EPSRC 主题：信息和通信技术 (ICT)、工程、数学科学和医疗保健技术，通过对这些主题内的以下研究领域做出重大贡献：数字信号处理、统计和应用概率。它将通过解决信号处理、信息理论和机器学习交叉领域的一系列重要研究问题，帮助保持英国在数据科学领域的学术卓越性。

Message passing algorithms are low-complexity algorithms that achieve state-of-the-art empirical performance in a variety of applications such as error correction and lossy compression. However, they lack theoretical performance guarantees in many of these applications. This project will analyse the performance of message algorithms by developing rigorous density evolution equations. We will start with the problem of lossy compression, and then extend the techniques to other approximation and inference problems.The project directly relates to several EPSRC themes: Information and Communications Technologies (ICT), Engineering, Mathematical Sciences, and Healthcare Technologies, by making a strong contribution to the following research areas within these themes: Digital Signal Processing, Statistics and Applied Probability. It will help maintain UK academic excellence in data science by addressing an important set of research questions at the intersection of signal processing, information theory, and machine learning.