7 citations · 27 across the 19 of their papers we have counts for
10 papers · 1 filter
Bayesian Sparse Gaussian Mixture Model in High Dimensions
Dapeng Yao, Fangzheng Xie, Yanxun Xu
We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is e…
Eigenvector-Assisted Statistical Inference for Signal-Plus-Noise Matrix Models
Fangzheng Xie, Dingbo Wu
In this paper, we develop a generalized Bayesian inference framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many application…
Entrywise limit theorems of eigenvectors for signal-plus-noise matrix models with weak signals
Fangzheng Xie
We establish a finite-sample Berry-Esseen theorem for the entrywise limits of the eigenvectors for a broad collection of signal-plus-noise random matrix models under challenging we…
Euclidean Representation of Low-Rank Matrices and Its Statistical Applications
Fangzheng Xie
Low-rank matrices are pervasive throughout statistics, machine learning, signal processing, optimization, and applied mathematics. In this paper, we propose a novel and user-friend…
Estimating the Penalty Level of -minimization via Two Gaussian Approximation Methods
Fang Xie
In this paper, we aim to give a theoretical approximation for the penalty level of -regularization problems. This can save much time in practice compared with the traditi…
Efficient Estimation for Random Dot Product Graphs via a One-step Procedure
Fangzheng Xie, Yanxun Xu
We propose a one-step procedure to estimate the latent positions in random dot product graphs efficiently. Unlike the classical spectral-based methods such as the adjacency and Lap…
Optimal Bayesian Estimation for Random Dot Product Graphs
Fangzheng Xie, Yanxun Xu
We propose a Bayesian approach, called the posterior spectral embedding, for estimating the latent positions in random dot product graphs, and prove its optimality. Unlike the clas…
A theoretical framework of the scaled Gaussian stochastic process in prediction and calibration
Mengyang Gu, Fangzheng Xie, Long Wang
Model calibration or data inversion is one of fundamental tasks in uncertainty quantification. In this work, we study the theoretical properties of the scaled Gaussian stochastic p…
A Theoretical Framework for Bayesian Nonparametric Regression
Fangzheng Xie, Wei Jin, Yanxun Xu
We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated -distance without assuming the regressio…
Adaptive Bayesian nonparametric regression using kernel mixture of polynomials with application to partial linear model
Fangzheng Xie, Yanxun Xu
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weig…