27 citations · 40 across the 14 of their papers we have counts for
14 papers
Differentially Private Manifold Denoising
Jiaqi Wu, Yiqing Sun, Zhigang Yao
We introduce a differentially private manifold denoising framework that allows users to exploit sensitive reference datasets to correct noisy, non-private query points without comp…
Ridge Estimation with Nonlinear Transformations
Zheng Zhai, Hengchao Chen, Zhigang Yao
Ridge estimation is an important manifold learning technique. The goal of this paper is to examine the effects of nonlinear transformations on the ridge sets. The main result prove…
Manifold Fitting in Ambient Space
Zhigang Yao, Bingjie Li, Wee Chin Tan
Modern sample points in many applications no longer comprise real vectors in a real vector space but sample points of much more complex structures, which may be represented as poin…
Manifold Fitting under Unbounded Noise
Zhigang Yao, Yuqing Xia
There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Re…
Quantifying Time-Varying Sources in Magnetoencephalography -- A Discrete Approach
Zhigang Yao, Zengyan Fan, Masahito Hayashi +1
We study the distribution of brain source from the most advanced brain imaging technique, Magnetoencephalography (MEG), which measures the magnetic fields outside the human head pr…
Community Detection Based on the convergence of eigenvectors in DCBM
Yan Liu, Zhiqiang Hou, Zhigang Yao +3
Spectral clustering is one of the most popular algorithms for community detection in network analysis. Based on this rationale, in this paper we give the convergence rate of eigenv…
Random Fixed Boundary Flows
Zhigang Yao, Yuqing Xia, Zengyan Fan
We consider fixed boundary flow with canonical interpretability as principal components extended on non-linear Riemannian manifolds. We aim to find a flow with fixed starting and e…
Sufficient Dimension Reduction for Classification
Xin Chen, Jingjing Wu, Zhigang Yao +1
We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired…
Principal Boundary on Riemannian Manifolds
Zhigang Yao, Zhenyue Zhang
We consider the classification problem and focus on nonlinear methods for classification on manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold…
Estimating the Number of Sources in Magnetoencephalography Using Spiked Population Eigenvalues
Zhigang Yao, Ye Zhang, Zhidong Bai +1
Magnetoencephalography (MEG) is an advanced imaging technique used to measure the magnetic fields outside the human head produced by the electrical activity inside the brain. Vario…
Principal Sub-manifolds
Zhigang Yao, Benjamin Eltzner, Tung Pham
We propose a novel method of finding principal components in multivariate data sets that lie on an embedded nonlinear Riemannian manifold within a higher-dimensional space. Our aim…
Partial Correlation Screening for Estimating Large Precision Matrices, with Applications to Classification
Shiqiong Huang, Jiashun Jin, Zhigang Yao
We propose Partial Correlation Screening (PCS) as a new row-by-row approach to estimating a large precision matrix . To estimate the -th row of , , PCS us…
A statistical approach to the inverse problem in magnetoencephalography
Zhigang Yao, William F. Eddy
Magnetoencephalography (MEG) is an imaging technique used to measure the magnetic field outside the human head produced by the electrical activity inside the brain. The MEG inverse…
Optimal classification in sparse Gaussian graphic model
Yingying Fan, Jiashun Jin, Zhigang Yao
Consider a two-class classification problem where the number of features is much larger than the sample size. The features are masked by Gaussian noise with mean zero and covarianc…