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math.ST2025
Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation
Xiuyuan Cheng, Nan Wu
This work studies the spectral convergence of graph Laplacian to the Laplace-Beltrami operator when the graph affinity matrix is constructed from random samples on a -dimens…
math.ST2025
Adaptive Bayesian Regression on Data with Low Intrinsic Dimensionality
Tao Tang, Nan Wu, Xiuyuan Cheng +1
We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function.…
math.ST2024
When Locally Linear Embedding Hits Boundary
Hau-tieng Wu, Nan Wu
Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud i…