"Ryan" Zheyuan Lai

Hi! I am an undergraduate student (2023 - 2027) at the National University of Singapore (NUS), pursuing majors in Statistics and Mathematics with a minor in Computer Science. Currently, I am fortunate to be supervised by Prof. Michael Choi, working on the intersection of stochastic processes and information theory.

My academic interests lie broadly in the theory and applications of statistical inference, stochastic processes, and machine learning. I am actively looking for research opportunities in these topics, please feel free to reach out to me if you have any openings, ideas, or just want to connect!

🔬 Research Interests

Markov chains and stochastic processes
Machine learning and generative modeling
Large language models (LLMs) and AI agents

📚 Selected Publications

Preprint

Information-theoretic subset selection of multivariate Markov chains via submodular optimization

Zheyuan Lai, and Michael CH Choi

arXiv preprint arXiv:2503.23340, 2025

Abs arXiv Code

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.