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Statistical Inference in Dynamical Systems

[Kernel ODE, ODE inference, SGD dynamics]

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

Xiaowu Dai and Yuhua Zhu. 

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

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

Xiaowu Dai and Lexin Li.​ 

Journal of the American Statistical Association: Theory and Methods (JASA), 2021.

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

Xiaowu Dai and Lexin Li. 

Preprint, 2022+.

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• Towards theoretical understanding of large batch training in stochastic gradient descent. [pdf]

Xiaowu Dai and Yuhua Zhu. 

Preprint, 2022+.

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• Nonparametric estimation via mixed gradients. [pdf]

Xiaowu Dai. 

Preprint, 2022+.

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