My research interests include:
Time-frequency analysis of nonstationary oscillatory time series;
Sparsity and variable selections;
Structure-informed (e.g., group symmetry, heavy tails, physical laws) machine learning: efficient algorithms and theoretical foundations, including finite-sample estimations, uncertainty quantification, and neural network approximation;
Regularized divergences, their information theory, gradient flows and convergence, and neural network-based algorithms for high-dimensional data.
Openings:
If you are an undergraduate student at UNC interested in doing summer research or an honors thesis with me, please contact me directly via email.
For prospective PhD students and postdoctoral researchers (those with a background in harmonic analysis, probability and stochastic analysis, signal processing or machine learning are particularly welcome), please contact me directly via email if you are interested.
My publications can also be found on my Google Scholar page.
Published Papers:
(with Hyemin Gu, Markos Katsoulakis, Luc Rey-Bellet and Wei Zhu), Robust Generative Learning with Lipschitz-Regularized α-Divergences Allows Minimal Assumptions on Target Distributions. To appear in Information and Inference: A Journal of the IMA.
(with Markos Katsoulakis, Luc Rey-Bellet and Wei Zhu), Statistical Guarantees of Group-Invariant GANs. SIAM/ASA Journal on Uncertainty Quantification, Vol. 13, Iss. 2 (2025), Pages 862-890.
(with Wei Zhu), On the Implicit Bias of Linear Equivariant Steerable Networks. Thirty-seventh Conference on Neural Information Processing Systems (NeurIPS 2023).
(with Markos Katsoulakis, Luc Rey-Bellet and Wei Zhu), Sample complexity of probability divergences under group symmetry. Fortieth International Conference on Machine Learning (ICML 2023), 4713-4734.
(with Hau-Tieng Wu), Disentangling modes with crossover instantaneous frequencies by synchrosqueezed chirplet transforms, from theory to application. Applied and Computational Harmonic Analysis, Volume 62, January 2023, Pages 84-122.
(with Hau-Tieng Wu), When Ramanujan meets time-frequency analysis in complicated time series analysis. Pure and Applied Analysis 4 (4), 629-673.
(with Yingzhou Li and Xiuyuan Cheng), SpecNet2: Orthogonalization-free spectral embedding by neural networks. The Third Mathematical and Scientific Machine Learning Conference (MSML 2022).
(with Anoopum Gupta, Zhuoqing Chang, Christopher Stephen, Jeremy Schmahmann, Hau-Tieng Wu and Guillermo Sapiro), Accurate Detection of Cerebellar Smooth Pursuit Eye Movement Abnormalities via Mobile Phone Video and Machine Learning. Scientific Reports 10, 18641 (2020).
Preprints:
(with Markos Katsoulakis and Benjamin Zhang), Equivariant score-based generative models provably learn distributions with symmetries efficiently, (2024)[arxiv]