于磊

• 2010年-2015年，中国科学技术大学，信息与通信工程博士 

• 2006年-2010年，中国科学技术大学，电子信息工程学士

• 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

  
  

于磊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信息工程专业博士毕业，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。

于磊目前从事信息论与概率论、组合数学等领域的交叉研究。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23篇（其中19篇为第一作者或单独作者的论文），其中15篇发表在IEEE Transactions on Information Theory（信息论顶刊）上，其他论文发表在Probability Theory and Related Fields（概率论顶刊）、Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques（概率论知名期刊）以及Journal of Combinatorial Theory, Series A（组合学知名期刊）等学术期刊上。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：Gray和Wyner于1974年提出DSBS的Gray-Wyner区域猜想、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）；同时于磊的研究也加强了经典的等周类型不等式和超压缩不等式，解决了Ordentlich-Polyanskiy-Shayevitz提出的强小集扩展猜想（2019）和Polyanskiy提出的强超压缩猜想（2016）。

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

      本人目前从事等周问题、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、信息论、组合数学等的交叉领域。

      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扩展定理（噪声稳定性）、FKN定理、KKL定理、不变性原理、超压缩不等式等等。 

       本人目前采用的研究方法主要为熵方法.  对熵的概念不了解的同学可以看一下我的科普报告的slides: “无处不在的熵”[slides]

• Online Short Course: Information Theory and Related Fields (every Wednesday during 4/12-6/14, 2023)

• Probability Theory, 2nd Semester, 2022-2023

• Mathematical Analysis (exercise class), 1st Semester, 2022-2023

• Probability Theory, 2nd Semester, 2021-2022

• Mathematical Analysis (exercise class), 1st Semester, 2021-2022

《高维泛函不等式及其应用》，国家自然科学基金青年基金，2022-2024

Monograph

1. Lei Yu, The Entropy Method, Preprint, Jul. 2023. [link] (Slides of this monograph can be found at the bottom of this homepage.)

2. 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][arxiv]

Journal Papers and Submitted Papers

1. Lei Yu and Hao Wu*, “Rényi–Sobolev Inequalities and Connections to Spectral Graph Theory”, Jun. 2023 [arxiv].

2. Lei Yu, “The entropy method in large deviation theory”, Oct. 2022 [arxiv], updated version [RG]. (Incorporated into the monograph “The Entropy Method”.)

3. Lei Yu, “Exact Exponents for Concentration and Isoperimetry in Product Polish Spaces”, May 2022. Updated Sep. 2022. [arxiv]
   * The exact exponents of the concentration and isoperimetric functions in the product Polish probability space were characterized in this paper, which verify an intimate connection among information theory, optimal transport, and concentration of measure or isoperimetric inequalities.

4. Lei Yu, Strong Brascamp-Lieb and Hypercontractivity Inequalities, Feb. 2021. Updated and submitted Sep. 2022. [arxiv][updated version]
   * This paper, motivated by the works in [link] and [link], strengthens classic Brascamp-Lieb and hypercontractivity inequalities, and also resolves Ordentlich-Polyanskiy-Shayevitz's conjecture in [link] and independently resolves Polyanskiy's conjecture stated in [link].(Refer to the monograph above for more information.)
   * The following paper is incorporated into the paper above.
   

5. Lei Yu, The Convexity and Concavity of Envelopes of the Minimum-Relative-Entropy Region for the DSBS, Jun. 2021. Updated Jul. 2022. [arxiv][updated version]

6. Lei Yu, Venkat Anantharam, and Jun Chen, Graphs of Joint Types, Noninteractive Simulation, and Stronger Hypercontractivity, Feb. 2021. Updated and submitted Jan. 2022. [arxiv]

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

8. Lei Yu, “Gray–Wyner and Mutual Information Regions for Doubly Symmetric Binary Sources and Gaussian Sources”, IEEE Trans. Inf. Theory, 2023. [arxiv]
   * This paper resolves a conjecture of Gray and Wyner in 1974

9. Lei Yu, “Dimension-Free Bounds for the Union-Closed Sets Conjecture,” Entropy (Invited Paper), 2023 [arxiv][MathematicaCode]
   * This paper numerically evaluates Sawin's bound on the Union-Closed Sets Conjecture which is 0.38234......

10. Lei Yu, “On the Φ-Stability and Related Conjectures,” Probability Theory and Related Fields, 2023. [arxiv]
    * This paper partially resolves the Mossel-O’Donnell Conjecture, the Courtade-Kumar Conjecture, and the Li-Médard Conjecture.

11. Jun Chen, Lei Yu, Jia Wang, Wuxian Shi, Yiqun Ge, Wen Tong, On the Rate-Distortion-Perception Function, IEEE Journal on Selected Areas in Information Theory, 2023.

12. Lei Yu and Venkat Anantharam, Sequential Channel Synthesis, IEEE Trans. Inf. Theory, 2023. [arxiv]

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

14. 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]

15. 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 resolves a problem posed by Elchanan Mossel in 2017.

16. 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 resolves a problem posed by Kumar, Li, and El Gamal in 2014.

17. 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]

18. 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.

19. 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]

20. 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]

21. 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.

22. 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]

23. 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]

24. 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]
    * An error exists in this paper, due to my negligence in the derivation. 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

25. 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.

26. 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]

27. 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]

28. 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]

29. 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]

30. 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]

Randomly Selected Invited Talks

1. “无处不在的熵”, 上海交通大学数学沙龙, May 2023 [slides]

2. “The Entropy Method”, Chinese Conference on Information Theory, Dec. 2022

3. “Noise Stability: Old and New”, Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Jul. 2022 [slides]

4. “On the Φ-Stability and Related Conjectures,” Shandong University, Apr. 2022

5. “Strong Brascamp-Lieb Inequalities,” ITW, Oct. 2021

6. “Common Information: Old and New”, Tutorial at the 2021 ISIT with Vincent Y. F. Tan, Jul. 2021. [slides of my part] (corrected version)

7. “Noninteractive simulation of binary random variables” (almost same as the 2nd part of the tutorial at the 2021 ISIT), School of Mathematics and Statistics, Kashgar University, China, Jul. 2021.

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

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

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

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

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

1. 信息论青年新星奖（中国电子学会），2022

2. “Common Information: Old and New”, Tutorial at the 2021 ISIT （信息论国际顶会） with Vincent Y. F. Tan, Jul. 2021.