7 papers
Learning manifold diffusion semigroups from graph transition matrices
Xiuyuan Cheng, Nan Wu
We consider graph diffusion processes constructed from finite i.i.d. samples drawn from an unknown manifold embedded in ambient Euclidean space, where the graph affinity is defined…
Improved convergence rate of kNN graph Laplacians: differentiable self-tuned affinity
Xiuyuan Cheng, Yixuan Tan, Nan Wu
In graph-based data analysis, -nearest neighbor (NN) graphs are widely used due to their adaptivity to local data densities. Allowing weighted edges in the graph, the kerneli…
Inferring manifolds using Gaussian processes
David B Dunson, Nan Wu
It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of non-linear structures, it is common to focus on Riemannian manifolds. M…
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…
Boundary Detection Algorithm Inspired by Locally Linear Embedding
Pei-Cheng Kuo, Nan Wu
In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedde…
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.…