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Statistical Foundations for Dynamical Models

[Optimization Dynamics, ODE and PDE Methods]

(Note:     students under my supervision;  † equal contribution;  * corresponding author)​​

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Optimization Dynamics​

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• On large batch training and sharp minima: A Fokker-Planck perspective. [journal][reprint][preprint]​[older version]

Xiaowu Dai and Yuhua Zhu. 

Journal of Statistical Theory and Practice (JSTP), special issue on "Advances in Deep Learning", 2020.

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ODE and PDE Methods

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• Kernel ordinary differential equations. [journal][reprint][preprint]

Xiaowu Dai and Lexin Li.​ 

Journal of the American Statistical Association: Theory and Methods (JASA), 2022. 

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• Post-regularization confidence bands for ordinary differential equations. [journal][preprint]

Xiaowu Dai​* and Lexin Li. 

Journal of Machine Learning Research (JMLR), 2024.

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• Nonparametric estimation via partial derivatives. [journal​][preprint]

Xiaowu Dai*. 

Journal of the Royal Statistical Society Series B: Statistical Methodology (JRSSB), 2024.

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• Quantifying microbial interactions based on compositional data using an iterative approach for solving Lotka-Volterra equations. 

Yue Huang, Tianqi Tang, Xiaowu Dai, and Fengzhu Sun.

Preprint, 2025.

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