26 citations · 32 across the 22 of their papers we have counts for
25 papers
Instance Optimal Sparse Recovery from Nonlinear Observations: A Unified Framework
Junren Chen, Arian Maleki
This paper develops a unified framework for instance optimal sparse recovery from nonlinear observations. The main ingredient is a signal-dependent restricted approximate invertibi…
Quantile Randomized Kaczmarz for Streaming Linear Systems with Massart Noise
Emeric Battaglia, Jian-Feng Cai, Junren Chen +3
Quantile randomized Kaczmarz (QRK) has proven to be an efficient solver for corrupted linear systems and has received much attention. It was recently shown by Cai et al. (SIAM J. M…
Minimax Optimal Estimator and Improved Error Rate for the MLE in Logistic Regression with Gaussian Design
Junren Chen, Arya Mazumdar
We study finite-sample parameter estimation in logistic regression with Gaussian design, where the goal is to estimate with f…
Near-Optimal Lower Bounds on One-Bit Compressed Sensing of Approximately Sparse Signals
Junren Chen, Arya Mazumdar, Ming Yuan
This paper provides the first near-optimal lower bounds for one-bit compressed sensing of approximately sparse signals lying in a scaled ball, which is a commonly adopted…
One-Bit Clustering for Two Component Sub-Gaussian Mixture Models
Junren Chen, Yun Yang
Clustering is a fundamental problem in statistics and machine learning. We propose the first one-bit clustering method for two-component sub-Gaussian mixture models. The method use…
Finite-Sample Performance of Gradient Descent in Logistic Regression with Gaussian Design
Junren Chen, Arya Mazumdar
We consider the parameter estimation problem in logistic regression with Gaussian design: the estimation of a fixed unknown parameter () from…
Low-Rank Tensor Estimation from Nonlinear Observations: A Unified Framework
Junren Chen, Lijun Ding, Dong Xia +1
We consider the estimation of a tensor of Tucker rank from the nonlinear observations $\{y_i=f_i(\langle A_i,X^\star\rangle)\}_{…
On the Subsample Size of Quantile-Based Randomized Kaczmarz
Jian-Feng Cai, Junren Chen, Anna Ma +1
Quantile-based randomized Kaczmarz (QRK) was recently introduced to efficiently solve sparsely corrupted linear systems [SIAM J. Mat…
Generalized Eigenvalue Problems with Generative Priors
Zhaoqiang Liu, Wen Li, Junren Chen
Generalized eigenvalue problems (GEPs) find applications in various fields of science and engineering. For example, principal component analysis, Fisher's discriminant analysis, an…
Robust Instance Optimal Phase-Only Compressed Sensing
Junren Chen, Michael K. Ng, Jonathan Scarlett
Phase-only compressed sensing (PO-CS) concerns the recovery of sparse signals from the phases of complex measurements. Recent results show that sparse signals in the standard spher…
Optimal Quantized Compressed Sensing via Projected Gradient Descent
Junren Chen, Ming Yuan
This paper provides a unified treatment to the recovery of structured signals living in a star-shaped set from general quantized measurements $\mathcal{Q}(\mathbf{A}\mathbf{x}-\mat…
One-Bit Phase Retrieval: Optimal Rates and Efficient Algorithms
Junren Chen, Ming Yuan
In this paper, we study the sample complexity and develop efficient optimal algorithms for 1-bit phase retrieval: recovering a signal from phaseless…
Uniform Recovery Guarantees for Quantized Corrupted Sensing Using Structured or Generative Priors
Junren Chen, Zhaoqiang Liu, Meng Ding +1
This paper studies quantized corrupted sensing where the measurements are contaminated by unknown corruption and then quantized by a dithered uniform quantizer. We establish unifor…
Exact Thresholds for Noisy Non-Adaptive Group Testing
Junren Chen, Jonathan Scarlett
In recent years, the mathematical limits and algorithmic bounds for probabilistic group testing have become increasingly well-understood, with exact asymptotic thresholds now being…
A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing
Junren Chen, Jonathan Scarlett, Michael K. Ng +1
In generative compressed sensing (GCS), we want to recover a signal from measurements () using a generative prior $\mathbf{x}^*\in G(\ma…
Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priors
Junren Chen, Michael K. Ng, Zhaoqiang Liu
The problem of recovering a signal from a quadratic system with full-rank ma…
A Parameter-Free Two-Bit Covariance Estimator with Improved Operator Norm Error Rate
Junren Chen, Michael K. Ng
A covariance matrix estimator using two bits per entry was recently developed by Dirksen, Maly and Rauhut [Annals of Statistics, 50(6), pp. 3538-3562]. The estimator achieves near…
Quantized Low-Rank Multivariate Regression with Random Dithering
Junren Chen, Yueqi Wang, Michael K. Ng
Low-rank multivariate regression (LRMR) is an important statistical learning model that combines highly correlated tasks as a multiresponse regression problem with low-rank priori…
Quantizing Heavy-tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recovery
Junren Chen, Michael K. Ng, Di Wang
This paper studies the quantization of heavy-tailed data in some fundamental statistical estimation problems, where the underlying distributions have bounded moments of some order.…
Phase Retrieval of Quaternion Signal via Wirtinger Flow
Junren Chen, Michael K. Ng
The main aim of this paper is to study quaternion phase retrieval (QPR), i.e., the recovery of quaternion signal from the magnitude of quaternion linear measurements. We show that…
Uniform Exact Reconstruction of Sparse Signals and Low-rank Matrices from Phase-Only Measurements
Junren Chen, Michael K. Ng
In phase-only compressive sensing (PO-CS), our goal is to recover low-complexity signals (e.g., sparse signals, low-rank matrices) from the phase of complex linear measurements. Wh…
Error Bound of Empirical Risk Minimization for Noisy Standard and Generalized Phase Retrieval Problems
Junren Chen, Michael K. Ng
In this paper, we study the estimation performance of empirical risk minimization (ERM) in noisy (standard) phase retrieval (NPR) given by , or noi…
High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization
Junren Chen, Cheng-Long Wang, Michael K. Ng +1
In this paper, we propose a uniformly dithered 1-bit quantization scheme for high-dimensional statistical estimation. The scheme contains truncation, dithering, and quantization as…
Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss
Junren Chen, Michael K. Ng
In this paper, we study color image inpainting as a pure quaternion matrix completion problem. In the literature, the theoretical guarantee for quaternion matrix completion is not…