沙龍名稱：西安"一帶一路"統(tǒng)計學和隨機理論及應(yīng)用國際科技合作基地系列報告

沙龍時間：12月13日14:00

沙龍地點：騰訊會議直播（ID:322 239 515 密碼：111111）

主辦單位：數(shù)學與統(tǒng)計學院

報告1：Neural Optimal Transport

講座人介紹：

Evgeny Burnaev是俄羅斯斯科爾科沃科技大學（Skoltech）的全職教授，博士生導師，也是該校應(yīng)用人工智能中心的主任。Evgeny Burnaev教授于2006年在莫斯科物理技術(shù)大學（MIPT）獲得理學碩士學位，2008年在信息傳播問題研究所獲得博士學位，2022年在莫斯科物理技術(shù)大學（MIPT）又獲得物理與數(shù)學博士學位。Evgeny Burnaev教授的研究興趣包括面向3D數(shù)據(jù)分析的深度學習、生成建模和流形（manifold）學習、替代建模和工業(yè)系統(tǒng)優(yōu)化等，相關(guān)研究被計算機科學的頂級會議如ICML, ICLR, NeurIPS, CVPR, ICCV, ECCV和期刊接收發(fā)表。

根據(jù)Google-Scholar的統(tǒng)計，Evgeny Burnaev教授的影響因子是33。Evgeny Burnaev教授2017年獲得青年科學家莫斯科政府獎，2019年在“幾何處理國際研討會”上獲得幾何處理數(shù)據(jù)集獎，2019年在IEEE Internet of People國際會議上獲最佳論文獎，2020年在 Int. Workshop on Artificial Neural Networks in Pattern Recognition國際研討會上獲最佳論文獎。自2007年，Evgeny Burnaev教授先后主持了多項跨國公司如Airbus, SAFT, IHI, Sahara Force India Formula 1 team等的工程項目，他和他的團隊開發(fā)的分析算法是元建模（metamodelling）和優(yōu)化中算法軟件庫的核心部分，且這個軟件庫獲得了Airbus最終的技術(shù)就緒水平證書（Technology Readiness Level certification）。根據(jù)Airbus專家評估，基于他們分析算法的軟件庫為航空器設(shè)計過程的很多方面節(jié)約了高達10%的時間和成本。

講座內(nèi)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.

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

講座人介紹：

Saeid Rezakhah 是伊朗德黑蘭阿米爾卡比爾理工大學副教授，博士生導師，1996年取得英國倫敦大學瑪麗皇后和韋斯特菲爾德學院（Queen Mary and Westfield College, University of London）概率統(tǒng)計博士學位，先后在美國密歇根州立大學和英國倫敦大學做訪問教授。Saeid Rezakhah教授研究興趣包括Selfsimilar Process; Hidden Markov Mixture models, Periodically Correlated Processes, Stable distributions, Random Polynomials; Time-Series Analysis; Stable Process和 Information Theory等等，目前在國際學術(shù)期刊發(fā)表sci檢索論文40余篇。

講座內(nèi)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.