Graph statistics: An emerging discipline in non-Euclidean data analysis
The explosive growth of complex data has catalyzed the emergence of graph statistics as a fundamentally new discipline in data science. Unlike traditional statistics, which operates primarily within the comfortable confines of Euclidean spaces, graph statistics confronts the reality that modern data naturally organize themselves as dynamic networks composed of complex interconnections. In this article, we present an overview of graph statistics as an emerging discipline, tracing its theoretical foundations, methodological innovations, and transformative applications. We examine how the integration of evolutionary game theory, ecological niche theory, topological data analysis, and graph theory through quasi-dynamic nonlinear modeling has created a new norm of statistical thinking capable of analyzing non-Euclidean data. We show how graph statistics is poised to revolutionize fields ranging from quantitative genetics and systems biology to materials science and artificial intelligence, offering a principled framework for transforming big data into practical knowledge.
讲师
日期
2026年09月14日 至 11月09日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周二 | 14:20 - 16:55 | Shuimo | ZOOM 01 | 928 682 9093 | BIMSA |
修课要求
Core competencies include fundamental statistics (linear models, statistical inference, experimental design, and computational statistics), foundational mathematics (ordinary differential equations, applied topology, Yau-Yau theory, and curvature theory), and computer programming.
课程大纲
Chapter 1 Fundamental Statistics
Chapter 2 Non-Euclidean Data
Chapter 3 Ecological Theory of Complex Systems
Chapter 4 Evolutionary Game Theory
Chapter 5 Quasi-dynamic Modeling and idopNetwork Inference
Chapter 6 Graph Representation of Complex Systems
Chapter 7 Developmental Modularity Theory and Modular Networks
Chapter 8 GLMY Dissection of idopNetworks
Chapter 9 Networks of Stochastic Complex Systems
Chapter 10 How idopNet Enables Artificial Intelligence
Chapter 11 Future Directions
Chapter 2 Non-Euclidean Data
Chapter 3 Ecological Theory of Complex Systems
Chapter 4 Evolutionary Game Theory
Chapter 5 Quasi-dynamic Modeling and idopNetwork Inference
Chapter 6 Graph Representation of Complex Systems
Chapter 7 Developmental Modularity Theory and Modular Networks
Chapter 8 GLMY Dissection of idopNetworks
Chapter 9 Networks of Stochastic Complex Systems
Chapter 10 How idopNet Enables Artificial Intelligence
Chapter 11 Future Directions
参考资料
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28. Kim, B. R., Zhang, L., Berg, A., Fan, J., & Wu, R. (2008). A computational approach to the functional clustering of periodic gene-expression profiles. Genetics, 180(2), 821-834.
29. Wang, Y., Xu, M., Wang, Z., Tao, M., Zhu, J., Wang, L., ... & Wu, R. (2012). How to cluster gene expression dynamics in response to environmental signals. Briefings in bioinformatics, 13(2), 162-174.
30. Pan, W., Che, J., & Wu, S. (2026). An improved method of Wu's functional clustering. Statistics Innovation, 3(1), e005.
31. George, E. I. (2000). The variable selection problem. Journal of the American Statistical Association, 95(452), 1304-1308.
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33. He, J. H., & Liu, J. F. (2009). Allometric scaling laws in biology and physics. Chaos, Solitons & Fractals, 41(4), 1836-1838.
34. Griffin, C., Jiang, L., & Wu, R. (2020). Analysis of quasi-dynamic ordinary differential equations and the quasi-dynamic replicator. Physica A: Statistical Mechanics and its Applications, 555, 124422.
35. Liu, S., Li, Z., Zhang, Y., & Yin, J. (2026). Exact recovery in the double sparse model: Sufficient and necessary signal conditions. Electronic Journal of Statistics, 20(1), 83-137.
36. Grigor'yan, A., Lin, Y., Muranov, Y., & Yau, S. T. (2012). Homologies of path complexes and digraphs. arXiv preprint arXiv:1207.2834.
37. Wu, S., & Zhang, M. (2025). Disentangling complex systems: IdopNetwork meets GLMY homology theory. Data Analytics and Topology, 1(2025), 47-64.
38. Wang, B., Feng, B., Lv, L., Li, S., & Pan, F. (2025). Structural feature extraction via topological data analysis. The Journal of Physical Chemistry Letters, 16(32), 8056-8067.
39. Vetrivel, S. C., Vidhyapriya, P., & Arun, V. P. (2025). The Challenges of Graph Neural Networks. In Graph Neural Networks: Essentials and Use Cases (pp. 79-108). Cham: Springer Nature Switzerland.
40. Zednik, C. (2021). Solving the black box problem: A normative framework for explainable artificial intelligence. Philosophy & technology, 34(2), 265-288.
41. Papillon, M., Sanborn, S., Mathe, J., Cornelis, L., Bertics, A., Buracas, D., ... & Miolane, N. (2025). Beyond euclid: An illustrated guide to modern machine learning with geometric, topological, and algebraic structures. Machine Learning: Science and Technology, 6(3), 031002.
42. Xiao, S., Wang, S., Dai, Y., & Guo, W. (2022). Graph neural networks in node classification: survey and evaluation. Machine Vision and Applications, 33(1), 4.
43. L’heureux, A., Grolinger, K., Elyamany, H. F., & Capretz, M. A. (2017). Machine learning with big data: Challenges and approaches. IEEE Access, 5, 7776-7797.
44. Ma, S., Dong, A., Zhou G., Yang, F., Long, F., Wang, Y., Yau, S.-T., Wu, R. (2026) IdopGNN: A graph statistical mechanics model of data prediction. Data Analytics and Topology (in press).
45. Yau, S. T., & Yau, S. S. T. (2000). Real time solution of nonlinear filtering problem without memory I. Mathematical Research Letters, 7(6), 671-693.
46. Yau, S. T., & Yau, S. S. T. (2008). Real time solution of the nonlinear filtering problem without memory II. SIAM Journal on Control and Optimization, 47(1), 163-195.
47. Wang, Y., Xu, S., Wei, X., Luo, X., Yau, S. S. T., Yau, S. T., & Wu, R. (2025). Yau-YauAL: A computer tool for solving nonlinear filtering problems. Data Analytics and Topology, 1 (2025), 77-84.
48. Xu, S., Wang, Y., Wu, S., Dong, A., Yau, S. S. T., Yau, S. T., & Wu, R. (2026). Statistical learning of stochastic complex systems via the Yau-Yau nonlinear filter. The Innovation, 7(6), 101267.
49. Lin, Y., Lu, L., & Yau, S. T. (2011). Ricci curvature of graphs. Tohoku Mathematical Journal, Second Series, 63(4), 605-627.
50. Opper, M., & Saad, D. (Eds.). (2001). Advanced mean field methods: Theory and practice. MIT press.
2. Christensen, R. (2018). Analysis of variance, design, and regression: Linear modeling for unbalanced data. Chapman and Hall/CRC.
3. Zhang, K., Liu, S., & Xiong, M. (2022). Changes from classical statistics to modern statistics and data science. arXiv preprint arXiv:2211.03756.
4. Martín, N. (2025). Data Science Versus Statistics. In International Encyclopedia of Statistical Science (pp. 621-623). Berlin, Heidelberg: Springer Berlin Heidelberg.
5. Carthew, R. W. (2021). Gene regulation and cellular metabolism: an essential partnership. Trends in Genetics, 37(4), 389-400.
6. Luo, L. (2021). Architectures of neuronal circuits. Science, 373(6559), eabg7285.
7. Barraclough, T. G. (2015). How do species interactions affect evolutionary dynamics across whole communities? Annual Review of Ecology, Evolution, and Systematics, 46(1), 25-48.
8. Wu, R., & Jiang, L. (2021). Recovering dynamic networks in big static datasets. Physics Reports, 912, 1-57.
9. Wu, S., Liu, X., Dong, A., Gragnoli, C., Griffin, C., Wu, J., ... & Wu, R. (2023). The metabolomic physics of complex diseases. Proceedings of the National Academy of Sciences, 120(42), e2308496120.
10. Feng, L., Gong, H., Zhang, S., Liu, X., Wang, Y., Che, J., ... & Wu, R. (2024). Hypernetwork modeling and topology of high-order interactions for complex systems. Proceedings of the National Academy of Sciences, 121(40), e2412220121.
11. Sun, L., Bian, Y., Yang, D., Miao, R., Meng, Y., Che, J., ... & Wu, R. (2026). Graph statistics theory of individualized quantitative genetics under haplotype-resolved genome assembly. Proceedings of the National Academy of Sciences, 123(14), e2600004123.
12. Chen, C., Jiang, L., Fu, G., Wang, M., Wang, Y., Shen, B., ... & Wu, R. (2019). An omnidirectional visualization model of personalized gene regulatory networks. NPJ systems biology and applications, 5(1), 38.
13. Dong, A., Wu, S., Che, J., Wang, Y., & Wu, R. (2023). idopNetwork: a network tool to dissect spatial community ecology. Methods in Ecology and Evolution, 14(9), 2272-2283.
14. Gong, H., Wang, H., Wang, Y., Zhang, S., Liu, X., Che, J., ... & Wu, R. (2024). Topological change of soil microbiota networks for forest resilience under global warming. Physics of Life Reviews, 50, 228-251.
15. Athreya, A., Fishkind, D. E., Tang, M., Priebe, C. E., Park, Y., Vogelstein, J. T., ... & Sussman, D. L. (2018). Statistical inference on random dot product graphs: a survey. Journal of Machine Learning Research, 18(226), 1-92.
16. Charikar, M., Chatziafratis, V., Niazadeh, R., & Yaroslavtsev, G. (2019, April). Hierarchical clustering for euclidean data. In The 22nd International Conference on Artificial Intelligence and Statistics (pp. 2721-2730). PMLR.
17. Song, W., Zhou, H., Zhou, Y., & Müller, H. G. (2026). Non-Euclidean data analysis with metric statistics. Harvard Data Science Review, 8.
18. Faraway, J. J. (2014). Regression for non-Euclidean data using distance matrices. Journal of Applied Statistics, 41(11), 2342-2357.
19. Yang, J., Xie, K., & An, N. (2022, August). Causal discovery on non-euclidean data. In Proceedings of the 28th ACM SIGKDD conference on knowledge discovery and data mining (pp. 2202-2211).
20. Smith, J. M., & Price, G. R. (1973). The logic of animal conflict. Nature, 246(5427), 15-18.
21. Su, Q., McAvoy, A., & Plotkin, J. B. (2023). Strategy evolution on dynamic networks. Nature Computational Science, 3(9), 763-776.
22. Sheng, A., Su, Q., Wang, L., & Plotkin, J. B. (2024). Strategy evolution on higher-order networks. Nature computational science, 4(4), 274-284.
23. Yeang, C. H., Huang, L. C., & Liu, W. C. (2012, August). Recurrent structural motifs reflect characteristics of distinct networks. In 2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (pp. 551-557). IEEE.
24. Newman, M. E. (2006). Modularity and community structure in networks. Proceedings of the national academy of sciences, 103(23), 8577-8582.
25. Ghavasieh, A., & De Domenico, M. (2024). Diversity of information pathways drives sparsity in real-world networks. Nature Physics, 20(3), 512-519.
26. Figueiredo, M. A., & Bioucas-Dias, J. M. (2012, May). Algorithms for imaging inverse problems under sparsity regularization. In 2012 3rd International Workshop on Cognitive Information Processing (CIP) (pp. 1-6). IEEE.
27. Bach, F., Jenatton, R., Mairal, J., & Obozinski, G. (2012). Optimization with sparsity-inducing penalties. Foundations and Trends in Machine Learning, 4(1), 1-106.
28. Kim, B. R., Zhang, L., Berg, A., Fan, J., & Wu, R. (2008). A computational approach to the functional clustering of periodic gene-expression profiles. Genetics, 180(2), 821-834.
29. Wang, Y., Xu, M., Wang, Z., Tao, M., Zhu, J., Wang, L., ... & Wu, R. (2012). How to cluster gene expression dynamics in response to environmental signals. Briefings in bioinformatics, 13(2), 162-174.
30. Pan, W., Che, J., & Wu, S. (2026). An improved method of Wu's functional clustering. Statistics Innovation, 3(1), e005.
31. George, E. I. (2000). The variable selection problem. Journal of the American Statistical Association, 95(452), 1304-1308.
32. Dong, A., Fa, C., Li, Z., Yau, S. T., & Wu, R. (2026). Multi-task learning of complex networks via nonlinear ordinary differential equations. Communications Physics.
33. He, J. H., & Liu, J. F. (2009). Allometric scaling laws in biology and physics. Chaos, Solitons & Fractals, 41(4), 1836-1838.
34. Griffin, C., Jiang, L., & Wu, R. (2020). Analysis of quasi-dynamic ordinary differential equations and the quasi-dynamic replicator. Physica A: Statistical Mechanics and its Applications, 555, 124422.
35. Liu, S., Li, Z., Zhang, Y., & Yin, J. (2026). Exact recovery in the double sparse model: Sufficient and necessary signal conditions. Electronic Journal of Statistics, 20(1), 83-137.
36. Grigor'yan, A., Lin, Y., Muranov, Y., & Yau, S. T. (2012). Homologies of path complexes and digraphs. arXiv preprint arXiv:1207.2834.
37. Wu, S., & Zhang, M. (2025). Disentangling complex systems: IdopNetwork meets GLMY homology theory. Data Analytics and Topology, 1(2025), 47-64.
38. Wang, B., Feng, B., Lv, L., Li, S., & Pan, F. (2025). Structural feature extraction via topological data analysis. The Journal of Physical Chemistry Letters, 16(32), 8056-8067.
39. Vetrivel, S. C., Vidhyapriya, P., & Arun, V. P. (2025). The Challenges of Graph Neural Networks. In Graph Neural Networks: Essentials and Use Cases (pp. 79-108). Cham: Springer Nature Switzerland.
40. Zednik, C. (2021). Solving the black box problem: A normative framework for explainable artificial intelligence. Philosophy & technology, 34(2), 265-288.
41. Papillon, M., Sanborn, S., Mathe, J., Cornelis, L., Bertics, A., Buracas, D., ... & Miolane, N. (2025). Beyond euclid: An illustrated guide to modern machine learning with geometric, topological, and algebraic structures. Machine Learning: Science and Technology, 6(3), 031002.
42. Xiao, S., Wang, S., Dai, Y., & Guo, W. (2022). Graph neural networks in node classification: survey and evaluation. Machine Vision and Applications, 33(1), 4.
43. L’heureux, A., Grolinger, K., Elyamany, H. F., & Capretz, M. A. (2017). Machine learning with big data: Challenges and approaches. IEEE Access, 5, 7776-7797.
44. Ma, S., Dong, A., Zhou G., Yang, F., Long, F., Wang, Y., Yau, S.-T., Wu, R. (2026) IdopGNN: A graph statistical mechanics model of data prediction. Data Analytics and Topology (in press).
45. Yau, S. T., & Yau, S. S. T. (2000). Real time solution of nonlinear filtering problem without memory I. Mathematical Research Letters, 7(6), 671-693.
46. Yau, S. T., & Yau, S. S. T. (2008). Real time solution of the nonlinear filtering problem without memory II. SIAM Journal on Control and Optimization, 47(1), 163-195.
47. Wang, Y., Xu, S., Wei, X., Luo, X., Yau, S. S. T., Yau, S. T., & Wu, R. (2025). Yau-YauAL: A computer tool for solving nonlinear filtering problems. Data Analytics and Topology, 1 (2025), 77-84.
48. Xu, S., Wang, Y., Wu, S., Dong, A., Yau, S. S. T., Yau, S. T., & Wu, R. (2026). Statistical learning of stochastic complex systems via the Yau-Yau nonlinear filter. The Innovation, 7(6), 101267.
49. Lin, Y., Lu, L., & Yau, S. T. (2011). Ricci curvature of graphs. Tohoku Mathematical Journal, Second Series, 63(4), 605-627.
50. Opper, M., & Saad, D. (Eds.). (2001). Advanced mean field methods: Theory and practice. MIT press.
听众
Undergraduate
, Advanced Undergraduate
, Graduate
, 博士后
, Researcher
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, 英文
讲师介绍
邬荣领，1995年获美国华盛顿大学（西雅图）数量遗传学博士学位，现任北京雁栖湖应用数学研究院研究员、清华大学丘成桐数学研究中心曾思明讲座教授，是国家杰青（B类）获得者、教育部长江讲座教授、中组部“国家特聘专家”、北京市科技战略人才。曾任美国宾夕法尼亚州立大学统计学、公共卫生科学杰出教授，统计遗传研究中心主任。入选美国科学促进会会士、美国统计学会会士，获美国应用数学与统计研究院（SAMSI）杰出研究员奖、美国农业荣誉协会“优秀青年学者”奖、佛罗里达大学研究基金教授奖、宾夕法尼亚州立大学杰出大学教授奖、Floyd科学创新等。目前担任Data Analytics and Topology、Statistics Innovation主编，多家遗传学、生物信息学、计算生物学领域期刊副主编、特约编辑和编委。研究兴趣包括：发展跨学科统计方法，揭示复杂性状及人类复杂疾病的遗传控制机理。提出的功能作图(Functional mapping)方法能有效发现性状发育的遗传规律，刻画基因效应随时空变化的关键模式。将功能作图与进化博弈论、尺度理论、食饵-捕食者理论相结合，发展出一系列计算方法用于构建从分子到表型的多层次、多空间、多刻度的基因型-表型关系立体网络，为系统生物学、系统医学、系统药物学研究提供分析工具。在Nature Reviews Genetics、Nature Communications、PNAS、Journal of the American Statistical Association、Annals of Applied Statistics、Physics of Life Reviews、Physics Reports、Briefings in Bioinformatics、Cell Reports、Evolution等国际重要刊物上发表SCI论文逾524篇，研究成果被Science、Cell等重要刊物引用或重点介绍。