光華講壇——社會名流與企業家論壇第6722期

主題：Approximate Bayesian Inference using Expectation Propagation (EP)（期望傳播的近似貝葉斯推理）

主講人：英國University of Defence and Research (UDRC) 姚丹研究員

主持人：計算機與人工智能學院 蔣太翔教授

時間：1月26日 10:30

會議地點：柳林校區經世樓D座 新財經綜合實驗室 206會議室

主辦單位：計算機與人工智能學院 新財經綜合實驗室 數字經濟與交叉科學創新研究院 科研處

主講人簡介：

姚丹，博士，現為英國University of Defence and Research (UDRC) research fellow。2015年本科畢業于成都理工大學，專業-地理信息系統。2018年碩士畢業于中國科學院遙感與數字地球研究所，碩士論文：基于低秩表示的高光譜圖像降噪算法。2022年博士畢業于英國Heriot-Watt University，博士論文: Expectation Propagation for Scalable Inverse Problems in Imaging。主要研究方向是使用期望傳播的近似貝葉斯算法及算法在不同圖像問題中的應用。研究成果發表于IEEE Transaction on Imaging Processing, SIAM Journal on Imaging Sciences, Optics Express等期刊。

內容提要：

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).

貝葉斯方法常用于解決不確定性量化對決策至關重要的估計問題。在使用貝葉斯推理解決高維逆問題時，計算精確的后驗分布通常是棘手的。為了應對這一挑戰，傳統方法使用馬爾可夫鏈蒙特卡洛(MCMC)算法來利用由此產生的后驗分布。然而，采樣過程意味著高計算成本，并且基于MCMC的算法(還)不能用于快速推理。基于變分推理(VI)的近似貝葉斯方法是吸引人的最先進的替代解決方案，旨在通過更簡單的分布來近似精確的后驗分布，與MCMC相比，其矩更容易計算，計算成本大大降低。在本次演講中，主講人將介紹一系列近似貝葉斯方法，稱為期望傳播(EP)。在第一部分中，主講人將討論EP的基本原理。在第二部分中，主講人將介紹一組新的可擴展和高效的EP算法，這些算法是可以用于解決不同的高維估計問題，包括：

(1)傳統的成像逆問題，如去噪、反卷積和壓縮感知(CS)；

(2)單光子光探測和測距(LiDAR)成像問題，例如，利用單光子雪崩二極管(SPADs)探測器和單光子激光雷達的貝葉斯神經形態成像測量對運動目標進行顏色恢復；

(3)脈沖神經網絡(SNN)的訓練。