Chenghui Li (李程晖)


PhD Student

Statistics

University of Wisconsin-Madison

1300 University Ave

Madison, WI 53706

cli539 AT wisc.edu


Github: chl781

I am a 5th year PhD student at University of Wisconsin-Madison. I am advised by Nicolás Gracía Trillos. Before that, I obtained my bachelor's degree in Math from Zhejiang University in 2019. My thesis was about a Minsum packing optimization problem supervised by Professor Zhiyi Tan. I got my master's degree in Statistics from University of Wisconsin-Madison in 2020 and master's degree in Math rom University of Wisconsin-Madison in 2025.

In my academic pursuits, I am interested in exploring topology and geometric perspectives to gain a deeper understanding of complex problems. This interest further motivates my study of algorithms and their concrete mathematical formulations. Additionally, I am passionate about designing fast and interpretable algorithms for statistical problems. My academic background is a diverse blend of mathematics, statistics, and computer science.

Working papers

  1. N. García Trillos*, S. Leo*, C. Li*, H. Li* “Central limit theorem on graph Laplacian Eigenvalue and Eigenvector estimation” In preparation

  2. N. García Trillos*, B. Hosseini*, C. Li* “Operator Learning on Grassmannian Manifold: from Distribution to Eigenfunction” In preparation

Preprints

  1. N. García Trillos*, C. Li*, R. Venkatraman “Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds”

  2. C. Li*, M. Neuman* “Consistency of augmentation graph and network approximability in contrastive learning”

  3. C. Li, J. Cisewski-Kehe “A divide-and-conquer approach to persistent homology”

  4. C. Li, R. Sonthalia, N. García Trillos “Spectral neural networks: approximation theory and optimization landscape”

  5. J. Zhao, C. Li, F. Sala, K. Rohe “Quantifying Structure in CLIP Embeddings: A Statistical Framework for Concept Interpretation”

Publications

  1. N. García Trillos*, P. He*, C. Li* “Large sample spectral analysis of graph-based multimanifold clustering” Journal of Machine Learning Research (JMLR) 24(143):1−71, 2023.

  2. J. Diakonikolas*, C. Li*, S. Padmanabhan*, C. Song* “A Fast Scale-Invariant Algorithm for Non-negative Least Squares with Non-negative Data” Neural Information Processing Systems (NeurIPS) 2022, 35: 6264-6277.

Workshops

  1. C. Li, R. Sonthalia, N. García Trillos, “The optimization landscape of Spectral neural network” ICML 2024 workshop: High-dimensional Learning Dynamics.

Teaching

  • Spring 2024 [TA]: STAT 301 Introduction To Statistical Methods

  • Fall 2023 [TA]: STAT 609 Mathematical Statistics I

  • Spring 2023 [TA]: STAT 324 Introductory Applied Statistics for Engineers

  • Fall 2022 [TA]: STAT 371 Introductory Applied Statistics for the Life Sciences

  • Fall 2020 [TA]: STAT 301 Introduction To Statistical Methods

  • Spring 2020 [Grader]: MATH 629 Introduction To Measure And Integration

Talks

  • Institute for Foudation of Data Science seminar, University of Wisconsin-Madison, Apr. 2025

  • Institute for Foudation of Data Science seminar, University of Wisconsin-Madison, Nov. 2024

  • Poster at DeepMath 2024, Philadelphia, Nov. 2024

  • Poster presentation and online talk at Neurips2023, New Orleans, Dec. 2023

  • Institute for Foudation of Data Science seminar, University of Wisconsin-Madison, Nov. 2023

  • Graph-based Techniques in Machine Learning minisymposium, Michigan State University, Oct. 2023

  • Geometry and topology seminar at Max Planck Institute for Mathematics, Leipzig Germany, June 2023

  • SIAM Conference on geometric and topological techniques in machine learning minisymposium, University State Utah, April 2023

  • Poster presentation and online talk at Neurips2022, New Orleans, Sep. 2022

  • Fall Workshop on Computational Geometry, Oct. 2021

  • Second Graduate Student Conference: Geometry and Topology meet Data Analysis and Machine Learning, July 2021

Service