Publications

(The authors are listed alphabetically.)

  1. When Locally Linear Embedding Hits Boundary
    (Hau-Tieng Wu and Nan Wu), accepted in Journal of Machine Learning Research, arXiv:1811.04423
  2. Length of a Shortest Closed Geodesic in Manifolds of Dimension Four
    (Nan Wu and Zhifei Zhu), Journal of Differential Geometry 122(3):519-564, November (2022).
  3. Data-driven Efficient Solvers for Langevin Dynamics on Manifold in High Dimensions
    (Yuan Gao, Jian-Guo Liu and Nan Wu), Applied and Computational Harmonic Analysis, Volume 62, January (2023), 261-309
  4. Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation
    (Xiuyuan Cheng and Nan), Applied and Computational Harmonic Analysis, Volume 61, November (2022), 132-190
  5. Graph Based Gaussian Process on Restricted Domains
    (David B Dunson, Hau-Tieng Wu and Nan Wu), Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 84, Issue 2, 2022, 414– 439
  6. Strong Uniform Consistency with Rates for Kernel Density Estimators with General Kernels on Manifolds
    (Hau-Tieng Wu and Nan Wu), Information and Inference: a Journal of the IMA, Volume 11, Issue 2, June (2022), 781–799
  7. Spectral Convergence of Graph Laplacian and Heat Kernel Reconstruction in $L^\infty$ from Random Samples
    (David B Dunson, Hau-Tieng Wu, and Nan Wu), Applied and Computational Harmonic Analysis, Volume 55, (2021) 282-336.
  8. An Upper Bound for the Smallest Area of a Minimal Surface in Manifolds of Dimension Four
    (Nan Wu and Zhifei Zhu), Journal of Geometric Analysis, Volume 30, (2020) 573-600.
  9. Connecting Dots-from Local Covariance to Empirical Intrinsic Geometry and Locally Linear Embedding
    (John Malik, Chao Shen, Hau-Tieng Wu, and Nan Wu), Pure and Applied Analysis, Volume 1 (2019), No. 4, 515-542.
  10. Think Globally and Fit Locally Under the Manifold Setup: Asymptotic Analysis of Locally Linear Embedding
    (Hau-Tieng Wu and Nan Wu), Annals of Statistics, Volume 46, Number 6B (2018), 3805-3837.

Preprints

(The authors are listed alphabetically.)

  1. Inferring Manifolds From Noisy Data Using Gaussian Processes
    (David B Dunson and Nan Wu). submitted, arXiv: 2110.07478