Research

Research Interest

My research primarily focuses on structural matrix estimation and network analysis, with broader interests in machine learning and statistical modeling. I am particularly interested in:

• High-dimensional statistical inference: Developing methods for estimating and analyzing large-scale structured matrices.

• Network analysis: Studying the structure and dynamics of complex networks, including community detection and spectral methods.

• Machine learning theory: Understanding the theoretical properties of learning algorithms in statistical settings.

I aim to develop theoretically sound and computationally efficient statistical methods that can be applied to real-world data in scientific and engineering domains.

Publications/Manuscripts

Entrywise Low-rank Matrix Estimation

• H. Yan and K. Levin (2025) Improved dependence on coherence in eigenvector and eigenvalue estimation error bounds AISTAT 2025

• H. Yan and K. Levin (2024) Coherence-free Entrywise Estimation of Eigenvectors in Low-rank Signal-plus-noise Matrix Models Neurips 2024

• H. Yan and K. Levin (2023) Minimax rates for latent position estimation in the generalized random dot product graph

Working projects

In-Context Learning

• Understanding how transformers develops in-context learning capability through gradient descent.

Multiple Matrix Estimation

• Revealing that multiple matrices with shared structures are much easier to estimate than a single matrix.