16 citations · 54 across the 16 of their papers we have counts for
18 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…
Forecast-Then-Optimize Deep Learning Methods
Jinhang Jiang, Nan Wu, Ben Liu +3
Time series forecasting underpins vital decision-making across various sectors, yet raw predictions from sophisticated models often harbor systematic errors and biases. We examine…
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…
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.…
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…
Informative Priors Improve the Reliability of Multimodal Clinical Data Classification
L. Julian Lechuga Lopez, Tim G. J. Rudner, Farah E. Shamout
Machine learning-aided clinical decision support has the potential to significantly improve patient care. However, existing efforts in this domain for principled quantification of…
Probabilistic Neural Transfer Function Estimation with Bayesian System Identification
Nan Wu, Isabel Valera, Fabian Sinz +3
Neural population responses in sensory systems are driven by external physical stimuli. This stimulus-response relationship is typically characterized by receptive fields, which ha…
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…
Almost sharp Sobolev trace inequalities in the unit ball under constraints
Xuezhang Chen, Wei Wei, Nan Wu
We establish three families of Sobolev trace inequalities of orders two and four in the unit ball under higher order moments constraint, and are able to construct \emph{smooth} tes…
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…
Graph Based Gaussian Processes on Restricted Domains
David B Dunson, Hau-Tieng Wu, Nan Wu
In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic…
Strong Uniform Consistency with Rates for Kernel Density Estimators with General Kernels on Manifolds
Hau-Tieng Wu, Nan Wu
When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be…
Spectral Convergence of Graph Laplacian and Heat Kernel Reconstruction in from Random Samples
David B Dunson, Hau-Tieng Wu, Nan Wu
In the manifold setting, we provide a series of spectral convergence results quantifying how the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions…
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…
Connecting Dots -- from Local Covariance to Empirical Intrinsic Geometry and Locally Linear Embedding
John Malik, Chao Shen, Hau-Tieng Wu +1
Local covariance structure under the manifold setup has been widely applied in the machine learning society. Based on the established theoretical results, we provide an extensive s…
Think globally, fit locally under the Manifold Setup: Asymptotic Analysis of Locally Linear Embedding
Hau-Tieng Wu, Nan Wu
Since its introduction in 2000, the locally linear embedding (LLE) has been widely applied in data science. We provide an asymptotical analysis of the LLE under the manifold setup.…
An upper bound for the smallest area of a minimal surface in manifolds of dimension four
Nan Wu, Zhifei Zhu
In this paper, we prove that for any closed 4-dimensional Riemannian manifold with trivial first homology group, if the Ricci curvature , the diameter $diam(M)\leq…
Length of a shortest closed geodesic in manifolds of dimension four
Nan Wu, Zhifei Zhu
In this paper, we show that for any closed 4-dimensional simply-connected Riemannian manifold with Ricci curvature , volume , and diameter ,…