Author

Jun-Ren Chen

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Preprint Sep 2026

Instance Optimal Sparse Recovery from Nonlinear Observations: A Unified Framework

This paper develops a unified framework for instance optimal sparse recovery from nonlinear observations. The main ingredient is a signal-dependent restricted approximate invertibility condition (RAIC) of some gradient, which leads to the instance optimality of iterative hard thresholding. Under Gaussian designs, we ap...

Jun-Ren Chen, A. Maleki · 2 citations

Preprint Aug 2026

Minimax Optimal Estimator and Improved Error Rate for the MLE in Logistic Regression with Gaussian Design

We study finite-sample parameter estimation in logistic regression with Gaussian design, where the goal is to estimate $\mathbf{\theta}^*\in \mathbb{R}^d$ with $R=\|\mathbf{\theta}^*\|_2\ge 1$ from i.i.d. samples $\{(\mathbf{x}_i,y_i)\}_{i=1}^n,$ $\mathbf{x}_i \sim N(0,\mathbf{I}_d)$, $y_i\mid \mathbf{x}_i \sim \mathrm...

Jun-Ren Chen, Arya Mazumdar · 0 citations

#machine learning Jun 2026

Finite-Sample Performance of Gradient Descent in Logistic Regression with Gaussian Design

The main technical component is to show that the gradient of the logistic loss satisfies a certain approximate invertibility condition (AIC) and uniformly control the deviation of the gradient from its population counterpart by covering and peeling arguments, and then show that the population GD is a contraction by a d...

Jun-Ren Chen, Arya Mazumdar · arXiv.org · 3 citations