Hoil Lee's homepage

Welcome

My name is Hoil Lee. I am a Ph.D. student in KAIST Dept of Mathematical Sciences. I study probability theory, and my advisor is Paul Jung.

Me in UCSB, for summer school “New tools for optimal mixing of Markov chains”

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Research interests

• Probability theory – Infinite and finite exchangeability, random graphs and graph limits (graphons).
• Statistical machine learning – Neural networks with heavy-tailed behavior.

Publications

1. François Caron, Fadhel Ayed, Paul Jung, Hoil Lee, Juho Lee, and Hongseok Yang, “Over-parameterised Shallow Neural Networks with Asymmetrical Node Scaling: Global Convergence Guarantees and Feature Learning”, submitted (arXiv:2302.01002).
2. Hoil Lee, Fadhel Ayed, Paul Jung, Juho Lee, Hongseok Yang, and François Caron, “Deep neural networks with dependent weights: Gaussian Process mixture limit, heavy tails, sparsity and compressibility”, accepted to Journal of Machine Learning Research. (arXiv:2205.08187)
3. Paul Jung, Hoil Lee, Jiho Lee, and Hongseok Yang, “-Stable convergence of heavy-tailed infinitely-wide neural networks”, to appear in Advances in Applied Probability. (doi:10.1017/apr.2023.3)

Talks

• “Infinitely wide neural networks”, seminar talk, 2022 KAIST Math Graduate student Seminar, September 2022, KAIST.
• “-Stable convergence of heavy-tailed infinitely-wide neural networks”, contributed talk, 2021 Korean Mathematical Society Annual meetings, October 2021, online.

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Solutions Manual to Probability: Theory and Examples, 5th edition, by R. Durrett

Wonjun Seo, my dear freind in UC Davis statistics, and I are working on a project where we make solutions to every exercise problem in Durrett’s Probability: Theory and Examples, 5th edition. Here is the latest (incomplete) version of it. (Last updated on Sep. 9, 2021)