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Sparse Principal Component Analysis and Iterative Thresholding
Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, itExpand
Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise. Expand
Sparse PCA: Optimal rates and adaptive estimation
Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of theExpand
Sparse CCA: Adaptive Estimation and Computational Barriers
Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originatedExpand
Achieving Optimal Misclassification Proportion in Stochastic Block Models
In this paper, we present a computationally feasible two-stage method that achieves optimal statistical performance in misclassification proportion for stochastic block model under weak regularity conditions. Expand
Nonparametric methods for doubly robust estimation of continuous treatment effects.
Continuous treatments (e.g., doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowingExpand
Optimal hypothesis testing for high dimensional covariance matrices
This paper considers testing a covariance matrixin the high dimensional setting where the dimension p can be comparable or much larger than the sample size n. The problem of testing the hypothesis H0Expand
Optimal estimation and rank detection for sparse spiked covariance matrices
This paper considers a sparse spiked covariance matrix model in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as theExpand
Accuracy of the Tracy–Widom limits for the extreme eigenvalues in white Wishart matrices
The distributions of the largest and the smallest eigenvalues of a $p$-variate sample covariance matrix $S$ are of great importance in statistics. Focusing on the null case where $nS$ follows theExpand
Computational Barriers in Minimax Submatrix Detection
This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. Expand