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于磊

统计与数据科学学院

个人资料

  • 部门: 统计与数据科学学院
  • 性别:
  • 出生年月:
  • 专业技术职务: 副教授
  • 研究标签:
  • 毕业院校: 中国科学技术大学
  • 学位: 博士
  • 学历:
  • 联系电话:
  • 电子邮箱: leiyu@nankai.edu.cn
  • 办公地址: 范孙楼339
  • 通讯地址:
  • 邮编:
  • 传真:

教育经历

  • 2010年-2015年,中国科学技术大学,电子工程博士 

  • 2006年-2010年,中国科学技术大学,电子工程学士


工作经历

  • Apr. 2021- Present, Associate Professor

    • School of Statistics and Data Science

    • Nankai University, Tianjin, China


  • Jan. 2020- Jan. 2021, Postdoc (with Prof. Venkat Anantharam)

    • Department of Electrical Engineering and Computer Sciences

    • University of California, Berkeley, USA


  • Jun. 2017- Dec. 2019, Research Fellow (with Prof. Vincent Y. F. Tan)

    • Department of Electrical and Computer Engineering

    • National University of Singapore, Singapore


  • Mar. 2016 – Apr. 2017, Visiting Scholar (with Prof. Chang Wen Chen)

    • State University of New York at Buffalo, Buffalo, NY, USA


  • Jul. 2015 – May 2017, Postdoctoral Researcher (with Prof. Houqiang Li)

    • Department of Electronic Engineering and Information Science

    • University of Science and Technology of China, Hefei, Anhui, China


  • Sep. 2014 – Dec. 2014, Visiting Student (supervised by Prof. Zixiang Xiong)

    • Texas A&M University, College Station, TX, USA




个人简介

于磊,男,于2021年入选南开大学“百名青年学科带头人培养计划”,成为南开大学统计与数据科学学院副教授、博士生导师

于磊2015年于中国科学技术大学电子工程专业博士毕业,之后依次于2015年、2017年以及2020年分别在中国科学技术大学、新加坡国立大学以及美国加州大学伯克利分校做博士后。

于磊目前从事等周问题、泛函不等式、最优输运等理论研究,该方向为概率论组合数学、信息论等的交叉领域。成果包括已发表专著一部《Common Information, Noise Stability, and Their Extensions》,以及在国际SCI期刊上发表论文18篇(其中15篇为第一作者或单独作者的论文),其中在信息论国际顶刊IEEE Transactions on Information Theory上发表13篇,在组合数学重要国际期刊Journal of Combinatorial Theory, Series A上发表1篇,在概率统计重要国际期刊Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques上发表1篇,以及在图像视频编码顶刊上发表3篇目前的研究中解决或部分解决多个公开问题与猜想,具体包括:Kumar, Li, and El Gamal于2014年提出的共信息问题、Mossel于2017年提出的1/4均值噪声稳定性问题、Mossel-O’Donnell猜想(2005)、Courtade-Kumar猜想(2013)、Li-Médard猜想(2018)等等;同时于磊的研究也加强了经典的等周不等式和超压缩不等式,解决了Ordentlich-Polyanskiy-Shayevitz提出的强小集拓展猜想及一般形式(2019)和Polyanskiy提出的强超压缩猜想及一般形式(2016)

本人的英文主页:https://leiyudotscholar.wordpress.com/


研究领域


      于磊目前从事等周问题、泛函不等式、最优输运、布尔函数分析等理论研究,该方向为概率论组合数学、信息论等的交叉领域。

      1. 等周问题起源于古希腊时期,是最经典的数学问题之一。对于一个平面上的封闭图形,我们可以定义它的周长和面积。给定周长,哪个图形的面积最大?不难想象,答案为圆盘。此问题即为等周问题。目前,经典等周问题已经繁衍出了很多变种问题,形成了一套理论,并且渗透到了概率、泛函、组合和理论计算机等领域。

      2. 泛函不等式一定程度上扩展了等周问题。如果把以上等周问题中的图形的示性函数替换成一般的(非负的)实值函数,那么我们就可以推导出一系列泛函不等式。这类泛函不等式一般具有对偶表达式,有助于我们解决对应的等周问题。此外研究泛函不等式本身也具有理论意义,在粒子物理、概率统计、理论计算机、信息论等领域有着重要应用。

      3. 最优输运理论是研究两个概率分布的最优“匹配”问题。该理论与等周问题和泛函不等式关系密切,并且在其他数学分支以及机器学习当中有着重要应用。

      4. 布尔函数是离散立方体的子集的示性函数,是最简单的离散函数。布尔函数在组合和理论计算机科学有着重要应用。布尔函数分析领域中的核心主题和定理包括小集拓展定理噪声稳定性)、FKN定理、KKL定理、不变性原理、超压缩不等式等等。 


教学工作

科研项目

论文著作

Monograph

Lei Yu and Vincent Y. F. Tan, Common Information, Noise Stability, and Their Extensions, Foundations and Trends® in Communications and Information Theory, Vol. 19, No. 2, Pages 107 – 389, 2022. [link]

Journal Papers and Submitted Papers

  1. Jun Chen, Lei Yu, Jia Wang, Wuxian Shi, Yiqun Ge, Wen Tong, “On the Rate-Distortion-Perception Function,” submitted, Apr. 2022.

  2. Lei Yu, “The Convexity and Concavity of Envelopes of the Minimum-Relative-Entropy Region for the DSBS,” Jun. 2021. [arxiv] This paper resolves (the original version of) Ordentlich-Polyanskiy-Shayevitz’s conjecture in [link] and independently resolves Polyanskiy’s conjecture stated in [link].

  3. Lei Yu, “On the Φ-Stability and Related Conjectures,” Apr. 2021. [arxiv] This paper partially solves the Mossel-O’Donnell Conjecture, the Courtade-Kumar Conjecture, and the Li-Médard Conjecture.

  4. Lei Yu, “Strong Brascamp-Lieb Inequalities,” Feb. 2021. [arxiv] This paper, motivated by the works in [link] and [link], strengthens classic Brascamp-Lieb and hypercontractivity inequalities.

  5. Lei Yu, Venkat Anantharam, and Jun Chen, “Graphs of Joint Types, Noninteractive Simulation, and Stronger Hypercontractivity,” Feb. 2021. [arxiv] This paper solves a weaker version of Ordentlich-Polyanskiy-Shayevitz’s conjecture in [link]. Short version was accepted to ISIT 2021.

  6. Lei Yu and Venkat Anantharam, “The Hypercontractivity Constant is the Largest Tensorized SDPI Constant for Binary Sources”, 2021.

  7. Lei Yu and Venkat Anantharam, “Sequential Channel Synthesis”, 2021.

  8. Lei Yu, Asymptotics for Strassen's Optimal Transport Problem, Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2022. [arxiv]

  9. Lei Yu, Edge-Isoperimetric Inequalities and Ball-Noise Stability: Linear Programming and Probabilistic Approaches, Journal of Combinatorial Theory, Series A, Volume 188, May 2022, 105583. [arxiv]

  10. Lei Yu and Vincent Y. F. Tan, “On Non-Interactive Simulation of Binary Random Variables” IEEE Trans. Inf. Theory, Vol. 67, No. 4, Pages 2528 – 2538, Apr 2021. [arxiv][slides] This paper solves a problem posed by Elchanan Mossel in 2017.

  11. Lei Yu and Vincent Y. F. Tan, “On exact and ∞-Rényi common informations,” IEEE Trans. Inf. Theory, Vol. 66, No. 6, Pages 3366 – 3406, Jun 2020. [arxiv][slides][slides] This paper solves a problem posed by Kumar, Li, and El Gamal in 2014.

  12. Lei Yu and Vincent Y. F. Tan, “Exact channel synthesis,” IEEE Trans. Inf. Theory, Vol. 66, No. 5, Pages 2299 – 2818, May 2020. [arxiv][slides]

  13. M. Baig, Lei Yu, Z. Xiong, A. Host-Madsen, H. Li, and W. Li, “On the Energy-Delay Tradeoff in Streaming Data: Finite Blocklength Analysis,” IEEE Trans. Inf. Theory, Vol. 66, No. 3, Pages 1861 – 1881, Mar 2020.

  14. Lei Yu and Vincent Y. F. Tan, “Simulation of random variables under Rényi divergence measures of all orders,” IEEE Trans. Inf. Theory, Vol. 65, No. 6, Pages 3349 – 3383, Jun 2019. [link][arxiv][slides]

  15. Lei Yu and Vincent Y. F. Tan, “Rényi resolvability and its applications to the wiretap channel,” IEEE Trans. Inf. Theory, Vol. 65, No. 3, Pages 1862– 1897, Mar 2019. [link][arxiv]

  16. Lei Yu and Vincent Y. F. Tan, “Asymptotic coupling and its applications in information theory,” IEEE Trans. Inf. Theory, Vol. 65, No. 3, Pages 1321– 1344, Mar 2019. [link][arxiv][slides] Conjecture 26 was disproved in [link]. Open Problem 1 was solved in [arxiv]. By using Kumagai-Hayashi’s proof ideas in [link], Open Problem 2 can be easily solved and Conjecture 25 can be easily disproved.

  17. Lei Yu, Houqiang Li, and Weiping Li, “Distortion bounds for source broadcast problems,” IEEE Trans. Inf. Theory, vol. 64, no. 9, pp. 6034-6053, Sep. 2018. [link][arxiv]

  18. Lin Zhou, Vincent Y. F. Tan, Lei Yu and Mehul Motani, “Exponential strong converse for content identification with lossy recovery,” IEEE Trans. Inf. Theory, vol. 64, no. 8, pp. 5879-5897, Aug 2018. [link][arxiv]

  19. Lei Yu and Vincent Y. F. Tan, “Wyner’s common information under Rényi divergence measures,” IEEE Trans. Inf. Theory, vol. 64, no. 5, pp. 3616-3632, May 2018. [link][arxiv] See Correction and New Converse in “Corrections to “Wyner’s Common Information under Rényi Divergence Measures”” IEEE Trans. Inf. Theory, Vol. 66, No. 4, Pages 2599 – 2608, Apr 2020

  20. Jian Shen, Lei Yu, Li Li, and Houqiang Li, “Foveation based wireless soft image delivery,” IEEE Trans. Multimedia, vol. 20, no. 10, pp. 2788 – 2800, May 2018.

  21. Lei Yu, Houqiang Li, and Weiping Li, “Joint source-channel secrecy using uncoded schemes: Towards secure source broadcast,” IEEE Trans. Inf. Theory, vol. 63, no. 11, pp. 7442-7463, Nov. 2017. [link][arxiv]

  22. Lei Yu, Houqiang Li, and Weiping Li, “Source-channel secrecy for Shannon cipher system,” IEEE Trans. Inf. Theory, vol. 63, no. 4, pp. 2596-2622, Apr. 2017. [link][arxiv][slides]

  23. Lei Yu, Houqiang Li, and Weiping Li, “Comments on ‘Approximate characterizations for the Gaussian source broadcast distortion region’,” IEEE Trans. Inf. Theory, vol. 62, no. 10, pp. 5966-5969, Oct. 2016. [link][arxiv]

  24. Lei Yu, Houqiang Li, and Weiping Li, “Wireless cooperative video coding using a hybrid digital-analog scheme,” IEEE Trans. Circuits Syst. Video Technol., vol. 25, no. 3, pp. 436-450, Mar. 2015. [link][pdf]

  25. Lei Yu, Houqiang Li, and Weiping Li, “Wireless scalable video coding using a hybrid digital-analog scheme,” IEEE Trans. Circuits Syst. Video Technol., vol. 24, no. 2, pp. 331-345, Feb. 2014. [link][pdf][matlab-code]


Conference Papers

  1. Lei Yu, Venkat Anantharam, and Jun Chen, “Type Graphs and Small-Set Expansion,” ISIT 2021.

  2. Lei Yu and Vincent Y. F. Tan, “Exact channel synthesis,” ISIT 2019.

  3. Lei Yu and Vincent Y. F. Tan, “On exact and ∞-Rényi common informations,” ISIT 2019.

  4. Lei Yu and Vincent Y. F. Tan, “Simulation of random variables under Rényi divergence measures of all orders,” ITW 2018. [arxiv][slides]

  5. Lei Yu, “Maximal guessing coupling and its applications,” ISIT 2018. [arxiv]

  6. Lei Yu and Vincent Y. F. Tan, “Wyner’s common information under Rényi divergence measures,” ISIT 2018. [link][arxiv]

  7. Lei Yu and Vincent Y. F. Tan, “Rényi resolvability and its applications to the wiretap channel,” Proceedings of the 10th International Conference on Information Theoretic Security (ICITS), 2017, Hong Kong, (Information Theoretic Security, Lecture Notes in Computer Science, pp 208-233, 2017). [link]

  8. Lei Yu, Houqiang Li, and Chang Wen Chen, “Distortion bounds for transmitting correlated sources with common part over MAC,” 54th Allerton Conference, Monticello, IL, USA, Sep. 2016. [arxiv]

  9. Lei Yu, Houqiang Li, and Weiping Li, “Source-channel secrecy for Shannon cipher system,” 54th Allerton Conference, Monticello, IL, USA, Sep. 2016. [arxiv]

  10. Lei Yu, Houqiang Li, and Weiping Li, “Distortion bounds for source broadcast over degraded channel,” IEEE Int. Symp. Inf. Theory (ISIT), Barcelona, Spain, Jul. 2016. [pdf]

  11. Jian Shen, Lei Yu, and Houqiang Li, “Hybrid digital-analog scheme for video transmission over fading channel,” IEEE Int. Symp. Circuits Syst. (ISCAS), Montreal, Canada, May 2016.

  12. Lei Yu, H. Li, W. Li, Z. Xiong, and A. Host-Madsen, “On the energy-delay tradeoff in lossy network communications,” IEEE Inf. Theory Workshop (ITW), Jeju Island, Korea, Oct. 2015. [matlab-code]

  13. Lei Yu, Houqiang Li, and Weiping Li, “Hybrid digital-analog scheme for video transmission over wireless,” IEEE Int. Symp. Circuits Syst. (ISCAS), pp. 1163-1166, Beijing, P. R. China, May 2013.


Notes and Unpublished Preprints

  1. Lei Yu and Vincent Y. F. Tan, “An Improved Linear Programming Bound on the Average Distance of a Binary Code,” Oct. 2019. [arxiv][slides]

  2. Lei Yu, “On Binary Maximal Correlation and Its Connections to Noise Stability,” Sep. 2019. [pdf]

  3. Lei Yu, “Information Spectrum, Concentration Spectrum, Rényi Transform, and Decomposition Problems,” Aug. 2019. [pdf]

  4. Lei Yu, “Deterministic Coupling Depends on Dimension,” Jun. 2019. [pdf]

  5. Lei Yu, “Universal simulation of random variables,” preprint, 2018. [arxiv][slides]

  6. Lei Yu, “On conditional correlations,” 2018. [arxiv]

  7. Lei Yu, Houqiang Li, and Chang Wen Chen, “Generalized common informations: Measuring commonness by the conditional maximal correction,” preprint, Oct. 2016. [arxiv][pdf]


Work Report

  1. Lei Yu, Some Problems in Information-Theoretic Security, May 2017. [pdf]

Invited Talks

  1. “Common Information: Old and New”, Tutorial at the 2021 ISIT with Vincent Y. F. Tan, Jul. 2021.

  2. “Average Distance and Boolean Function”, Institute for Mathematical Sciences, ShanghaiTech University, China, Dec. 2019.

  3. “Asymptotics for Strassen’s Optimal Transport Problem”, Institute for Mathematical Sciences, ShanghaiTech University, China, Dec. 2019.

  4. “On Binary Codes and Non-Interactive Simulation”, Workshop on Probability and Information Theory, The University of Hong Kong, China, Aug. 2019.

  5. “On exact and ∞-Rényi common informations,” ITA, Feb. 2019.

  6. “Joint source-channel coding,” McMaster University, Canada, Dec. 1, 2016.

学术交流

荣誉奖励

学术成果

学位: 博士

毕业院校: 中国科学技术大学

邮件: leiyu@nankai.edu.cn

办公地点: 范孙楼339

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出生年月:

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