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Sparse Principal Component Analysis and Iterative Thresholding
- Zongming Ma
- Computer Science
- 12 December 2011
Under a spiked covariance model, a new iterative thresholding approach for estimating principal subspaces in the setting where the leading eigenvectors are sparse is proposed and it is found that the new approach recovers the principal subspace and leading eignevectors consistently, and even optimally, in a range of high-dimensional sparse settings.
Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow
A novel thresholded gradient descent algorithm is proposed and it is shown to adaptively achieve the minimax optimal rates of convergence over a wide range of sparsity levels when the a_j's are independent standard Gaussian random vectors, provided that the sample size is sufficiently large compared to the sparsity of $x.
Sparse PCA: Optimal rates and adaptive estimation
Under mild technical conditions, this paper establishes the optimal rates of convergence for estimating the principal subspace which are sharp with respect to all the parameters, thus providing a complete characterization of the difficulty of the estimation problem in term of the convergence rate.
Non‐parametric methods for doubly robust estimation of continuous treatment effects
- Edward H. Kennedy, Zongming Ma, M. McHugh, D. Small
- Mathematics, EconomicsJournal of The Royal Statistical Society Series B…
- 2 July 2015
A novel kernel smoothing approach is developed that requires only mild smoothness assumptions on the effect curve, and still allows for misspecification of either the treatment density or outcome regression.
Achieving Optimal Misclassification Proportion in Stochastic Block Models
- Chao Gao, Zongming Ma, A. Zhang, Harrison H. Zhou
- Computer ScienceJournal of machine learning research
- 14 May 2015
A computationally feasible two-stage method that achieves optimal statistical performance in misclassification proportion for stochastic block model under weak regularity conditions and is demonstrated by competitive numerical results.
Sparse CCA: Adaptive Estimation and Computational Barriers
It is shown that a sample size condition is needed for any randomized polynomial-time estimator to be consistent, assuming hardness of certain instances of the Planted Clique detection problem.
Optimal estimation and rank detection for sparse spiked covariance matrices
- T. Cai, Zongming Ma, Yihong Wu
- Computer Science, MathematicsProbability theory and related fields
- 14 May 2013
The optimal rate of convergence for estimating the spiked covariance matrix under the spectral norm is established, which requires significantly different techniques from those for estimating other structured covariance matrices such as bandable or sparse covariances matrices.
Optimal hypothesis testing for high dimensional covariance matrices
This paper considers testing a covariance matrix in the high dimensional setting where the dimension p can be comparable or much larger than the sample size n and introduces a test based on a U -statistic, which is shown to be rate optimal over this asymptotic regime.
Accuracy of the Tracy–Widom limits for the extreme eigenvalues in white Wishart matrices
- Zongming Ma
- 1 February 2012
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 the…
Structural Learning of Chain Graphs via Decomposition.
- Zongming Ma, X. Xie, Z. Geng
- Computer ScienceJournal of machine learning research : JMLR
- 1 December 2008
Simulations under a variety of settings demonstrate the competitive performance of the proposed computationally feasible method for the structural learning of chain graphs based on the idea of decomposing the learning problem into a set of smaller scale problems on its decomposed subgraphs.