Approximate Bayesian Inference using Expectation Propagation (EP)（期望传播的近似贝叶斯推理）

光华讲坛——社会名流与企业家论坛第6722期

主题：Approximate Bayesian Inference using Expectation Propagation (EP)（期望传播的近似贝叶斯推理）

主讲人：英国University of Defence and Research (UDRC) 姚丹研究员

主持人：计算机与人工智能学院 蒋太翔教授

时间：1月26日 10:30

会议地点：柳林校区经世楼D座 新财经综合实验室 206会议室

主办单位：计算机与人工智能学院 新财经综合实验室 数字经济与交叉科学创新研究院 科研处

主讲人简介：

姚丹，博士，现为英国University of Defence and Research (UDRC) research fellow。2015年本科毕业于成都理工大学，专业-地理信息系统。2018年硕士毕业于中国科学院遥感与数字地球研究所，硕士论文：基于低秩表示的高光谱图像降噪算法。2022年博士毕业于英国Heriot-Watt University，博士论文: Expectation Propagation for Scalable Inverse Problems in Imaging。主要研究方向是使用期望传播的近似贝叶斯算法及算法在不同图像问题中的应用。研究成果发表于IEEE Transaction on Imaging Processing, SIAM Journal on Imaging Sciences, Optics Express等期刊。

内容提要：

Bayesian methods are commonly used to solve estimation problems where uncertainty quantification is critical for decision making. To solve high-dimensional inverse problems using Bayesian inference, computing the exact posterior distribution is usually intractable. To address this challenge, Markov chain Monte Carlo (MCMC) algorithms have been traditionally proposed to exploit the resulting posterior distribution. However, the sampling process implies a high computational cost and MCMC-based algorithms are not (yet) scalable for fast inference. Approximate Bayesian methods based on variational inference (VI) are attractive state-of-the-art alternative solutions which aim at approximating the exact posterior distribution by a simpler distribution whose moments are easier to compute with a much reduced computational cost compared to MCMC. In this talk, I will introduce a family of approximate Bayesian methods called Expectation Propagation (EP). In the first part, I will discuss the basic principles of EP. In the second part, I will present a set of new scalable and efficient EP algorithms that I have been developed to solve different high-dimensional estimation problems, including (1) the traditional imaging inverse problems such as denoising, deconvolution, and compressive sensing (CS), (2) single-photon Light Detection and Ranging (LiDAR) imaging problems, such as color restoration of moving objects using measurements from Single-Photon Avalanche Diodes (SPADs) detector and Bayesian neuromorphic imaging for single-photon LiDAR, and (3) the training of Spiking Neural Networks (SNN).

贝叶斯方法常用于解决不确定性量化对决策至关重要的估计问题。在使用贝叶斯推理解决高维逆问题时，计算精确的后验分布通常是棘手的。为了应对这一挑战，传统方法使用马尔可夫链蒙特卡洛(MCMC)算法来利用由此产生的后验分布。然而，采样过程意味着高计算成本，并且基于MCMC的算法(还)不能用于快速推理。基于变分推理(VI)的近似贝叶斯方法是吸引人的最先进的替代解决方案，旨在通过更简单的分布来近似精确的后验分布，与MCMC相比，其矩更容易计算，计算成本大大降低。在本次演讲中，主讲人将介绍一系列近似贝叶斯方法，称为期望传播(EP)。在第一部分中，主讲人将讨论EP的基本原理。在第二部分中，主讲人将介绍一组新的可扩展和高效的EP算法，这些算法是可以用于解决不同的高维估计问题，包括：

(1)传统的成像逆问题，如去噪、反卷积和压缩感知(CS)；

(2)单光子光探测和测距(LiDAR)成像问题，例如，利用单光子雪崩二极管(SPADs)探测器和单光子激光雷达的贝叶斯神经形态成像测量对运动目标进行颜色恢复；

(3)脉冲神经网络(SNN)的训练。