Wenjing Liao 

Assistant Professor
School of Mathematics
Georgia Institute of Technology
Office: Skiles 258
Email: wliao60@gatech.edu

My research interests are imaging, signal processing,  high dimensional data analysis and machine learning. I finished my Ph.D. in Mathematics under the supervision of Prof. Albert Fannjiang at University of California, Davis. I was a visiting assistant professor at Duke University and an assistant research scientist at Johns Hopkins University before joining Georgia Tech. I worked with Prof. Mauro Maggioni at Duke and JHU. My research is supported by NSF DMS 1818751, DMS 2012652 and NSF CAREER.

I am looking for motivated students who are interested in deep learning theory, manifold learning, PDE identification and super-resolution in imaging.  Please send me an email if you are interested.

Teaching at GaTech: 
  • Math 6643 in Fall 2022

Editorial service:  Guest editor for a special issue in Sampling Theory, Signal Processing, and Data Analysis, deadline on December 31st, 2022, submit now!

Publications:  Google Scholar

Deep learning theory

denotes equal contributions

  1. On deep generative models for approximation and estimation of distributions on manifolds, NeurIPS 2022.
    Biraj Dahal*, Alex Havrilla*, Minshuo Chen, Tuo Zhao, Wenjing Liao
  2. A manifold two-sample test study: integral probability metric with neural networks, arXiv, 2022.
    Jie Wang, Minshuo Chen, Tuo Zhao, Wenjing Liao, Yao Xie
  3. Benefits of overparametrized convolutional residual networks: function approximation under smoothness constraint, ICML 2022.
    Hao Liu, Minshuo Chen, Siawpeng Er, Wenjing Liao, Tong Zhang, Tuo Zhao
  4. Deep nonparametric estimation of operators between infinite dimensional spaces, arXiv, 2022.
    Hao Liu, Haizhao Yang, Minshuo Chen, Tuo Zhao, Wenjing Liao
  5. Nonparametric regression on low-dimensional manifolds using deep ReLU networks, IMA Information and Inference, 2022.
    Minshuo Chen, Haoming Jiang, Wenjing Liao, Tuo Zhao
  6. Doubly robust off-policy learning on low-dimensional manifolds by deep neural networks, arXiv, 2021
    Minshuo Chen*, Hao Liu*, Wenjing Liao, Tuo Zhao
  7. Besov function approximation and binary classification on low-dimensional manifolds using convolutional residual networks, ICML, 2021.
    Hao Liu, Minshuo Chen, Tuo Zhao, Wenjing Liao
  8. Statistical guarantees of generative adversarial networks for distribution estimation, arXiv, 2020.
    Minshuo Chen, Wenjing Liao, Hongyuan Zha, Tuo Zhao
  9. Efficient approximation of deep ReLU networks for functions on low dimensional manifolds, NeurIPS 2019.
    Minshuo Chen, Haoming Jiang, Wenjing Liao, Tuo Zhao

Manifold learning

  1. Multiscale regression on unknown manifolds, Mathematics in Engineering, 2022.
    Wenjing Liao, Mauro Maggioni, Stefano Vigogna
  2. Adaptive geometric multiscale approximations for intrinsically low-dimensional data, Journal of Machine Learning Research, 2020.
    Wenjing Liao, Mauro Maggioni
  3. Learning adaptive multiscale approximations to data and functions near low-dimensional sets, Proceedings of the IEEE Information Theory Workshop 2016
    Wenjing Liao, Mauro Maggioni,
    Stefano Vigogna

PDE identification from noisy data
  1. Robust PDE identification from noisy data, SIAM Journal on Scientific Computing, 2022.
    Yuchen He, Sung Ha Kang, Wenjing Liao, Hao Liu, Yingjie Liu
  2. Identifying Di fferential Equations with Numerical Time evolution, Journal of Scientific Computing, 2021.
    Sung Ha Kang, Wenjing Liao, Yingjie Liu
  3. Numerical identification of nonlocal potential aggregation, Communication in Computational Physics, 2022.
    Yuchen He, Sung Ha Kang, Wenjing Liao, Hao Liu, Yingjie Liu

Grid-independent imaging and super-resolution
  1. Stability and super-resolution of MUSIC and ESPRIT for multi-snapshot spectral estimation, IEEE Transactions on Signal Processing, 2022.
    Weilin Li, Zengying Zhu, Weiguo Gao, Wenjing Liao
  2. Super-resolution limit of the ESPRIT algorithmIEEE Transactions on Information Theory 2020.
    Weilin Li, Wenjing Liao, Albert Fannjiang
  3. Conditioning of restricted Fourier matrices and super-resolution of MUSIC, Proceeding of the Sampling Theory and Applications, 2019.
    Weilin Li, Wenjing Liao
  4. Stable super-resolution limit and smallest singular value of restricted Fourier matrices, Applied and Computational Harmonic Analysis (ACHA), 2020. [ACHA 2021 Charles Chui Young Researcher Best Paper Award]
    Weilin Li, Wenjing Liao
  5. Sensor calibration for off-the-grid spectral estimation, Applied and Computational Harmonic Analysis, 2018.
    Yonina Eldar, Wenjing Liao, Sui Tang
  6. MUSIC for single-snapshot spectral estimation: stability and super-resolution, Applied and Computational Harmonic Analysis (ACHA), 2016. [One of the top downloaded papers in ACHA]
    Wenjing Liao, Albert Fannjiang
  7. MUSIC for multidimensional spectral estimation: stability and super-resolution, IEEE Transactions on Signal Processing, 2015
    Weilin Li, Wenjing Liao
  8. MUSIC for joint frequency estimation: stability with compressive measurements, Proceedings of the IEEE Global Conference on Signal and Information Processing, 2014.
    Wenjing Liao
  9. Coherence-pattern guided compressive sensing with unresolved grids, SIAM Journal on Imaging Sciences, 2012.
    Albert Fannjiang, Wenjing Liao
  10. Super-resolution by compressive sensing algorithms, 2012 Asilomar Conference on Signals, Systems and Computers.
    Albert Fannjiang, Wenjing Liao
  11. Mismatch and resolution in compressive imaging, Wavelets and Sparsity XIV, Proceedings of SPIE, 2011.
    Albert Fannjiang, Wenjing Liao

Fourier phase retrieval

  1. Fourier phasing with phase-uncertain mask, Inverse Problems, 2013. [Matlab code]
    Albert Fannjiang, Wenjing Liao
  2. Phase retrieval with random phase illumination, Journal of the Optical Society of America, 2012. Top 5 of the most downloaded articles on image processing from JOSA A and Optical Express over 2012 and 2013. [Matlab code]
    Albert Fannjiang, Wenjing Liao
  3. Compressed sensing phase retrieval, 2011 Asilomar Conference on Signals, Systems and Computers.
    Albert Fannjiang, Wenjing Liao