西安"一带一路"统计学和随机理论及应用国际科技合作基地系列报告

沙龙名称：西安"一带一路"统计学和随机理论及应用国际科技合作基地系列报告

沙龙时间：12月13日14:00

沙龙地点：腾讯会议直播（ID:322 239 515 密码：111111）

主办单位：数学与统计学院

报告1：Neural Optimal Transport

讲座人介绍：

Evgeny Burnaev是俄罗斯斯科尔科沃科技大学（Skoltech）的全职教授，博士生导师，也是该校应用人工智能中心的主任。Evgeny Burnaev教授于2006年在莫斯科物理技术大学（MIPT）获得理学硕士学位，2008年在信息传播问题研究所获得博士学位，2022年在莫斯科物理技术大学（MIPT）又获得物理与数学博士学位。Evgeny Burnaev教授的研究兴趣包括面向3D数据分析的深度学习、生成建模和流形（manifold）学习、替代建模和工业系统优化等，相关研究被计算机科学的顶级会议如ICML, ICLR, NeurIPS, CVPR, ICCV, ECCV和期刊接收发表。

根据Google-Scholar的统计，Evgeny Burnaev教授的影响因子是33。Evgeny Burnaev教授2017年获得青年科学家莫斯科政府奖，2019年在“几何处理国际研讨会”上获得几何处理数据集奖，2019年在IEEE Internet of People国际会议上获最佳论文奖，2020年在 Int. Workshop on Artificial Neural Networks in Pattern Recognition国际研讨会上获最佳论文奖。自2007年，Evgeny Burnaev教授先后主持了多项跨国公司如Airbus, SAFT, IHI, Sahara Force India Formula 1 team等的工程项目，他和他的团队开发的分析算法是元建模（metamodelling）和优化中算法软件库的核心部分，且这个软件库获得了Airbus最终的技术就绪水平证书（Technology Readiness Level certification）。根据Airbus专家评估，基于他们分析算法的软件库为航空器设计过程的很多方面节约了高达10%的时间和成本。

讲座内容：

Solving optimal transport (OT) problems with neural networks has become widespread in machine learning. The majority of existing methods compute the OT cost and use it as the loss function to update the generator in generative models (Wasserstein GANs). In this presentation, I will discuss the absolutely different and recently appeared direction - methods to compute the OT plan (map) and use it as the generative model itself. Recent advances in this field demonstrate that they provide comparable performance to WGANs. At the same time, these methods have a wide range of superior theoretical and practical properties.

The presentation will be mainly based on our recent pre-print "Neural Optimal Transport" https://arxiv.org/abs/2201.12220. I am going to present a neural algorithm to compute OT plans (maps) for weak & strong transport costs. For this, I will discuss important theoretical properties of the duality of OT problems that make it possible to develop efficient practical learning algorithms. Besides, I will prove that neural networks actually can approximate transport maps between probability distributions arbitrarily well. Practically, I will demonstrate the performance of the algorithm on the problems of unpaired image-to-image style transfer and image super-resolution.

报告2：Semi-Levy driven CARMA process: Estimation and Prediction

讲座人介绍：

Saeid Rezakhah 是伊朗德黑兰阿米尔卡比尔理工大学副教授，博士生导师，1996年取得英国伦敦大学玛丽皇后和韦斯特菲尔德学院（Queen Mary and Westfield College, University of London）概率统计博士学位，先后在美国密歇根州立大学和英国伦敦大学做访问教授。Saeid Rezakhah教授研究兴趣包括Selfsimilar Process; Hidden Markov Mixture models, Periodically Correlated Processes, Stable distributions, Random Polynomials; Time-Series Analysis; Stable Process和 Information Theory等等，目前在国际学术期刊发表sci检索论文40余篇。

讲座内容：

The Levy driven Continuous-time ARMA (CARMA) models are restricted for modeling stationary processes. In this talk, we introduce semi-Levy driven CARMA (SL-CARMA) process as a generalized form of SL-CAR model which establishes a class of periodically correlated process. By a new representation of the semi-Levy process, we provide a ? discretized state-vector process with independent periodically identically distributed noise corresponding to high-frequency data. Then, we estimate
the parameters of the SL-CARMA process by Kalman filtering method. By simulation studies, the accuracy of the estimated parameters of a general form of semi-Levy and a special case of Normal inverse Gaussian backdriving processes are evaluated. Finally, the SL-CARMA process have much better fitting to the periodically correlated process in compare to the retrieved Levy driven CARMA models by applying periodic sample from the Apnea-ECG database and the percent log returns of Dow-Jones Industrial Average indices by mean absolute error criteria and Diebold-Mariano test.