Search Results - "Cai, T. T."

OPTIMAL RATES OF CONVERGENCE FOR NOISY SPARSE PHASE RETRIEVAL VIA THRESHOLDED WIRTINGER FLOW by Cai, T. Tony, Li, Xiaodong, Ma, Zongming

“…This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal x ϵ ℝp from noisy quadratic measurements yj = (a′jx)² + εj, j = 1 , …”
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Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise by Cai, T. T., Lie Wang

“…We consider the orthogonal matching pursuit (OMP) algorithm for the recovery of a high-dimensional sparse signal based on a small number of noisy linear…”
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Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models by Ma, Rong, Tony Cai, T., Li, Hongzhe

“…High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this article, global testing and large-scale multiple testing…”
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RATE-OPTIMAL PERTURBATION BOUNDS FOR SINGULAR SUBSPACES WITH APPLICATIONS TO HIGH-DIMENSIONAL STATISTICS by Cai, T. Tony, Zhang, Anru

“…Perturbation bounds for singular spaces, in particular Wedin’s sin Θ theorem, are a fundamental tool in many fields including high-dimensional statistics,…”
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Transfer learning for nonparametric classification: Minimax rate and adaptive classifier by Cai, T. Tony, Wei, Hongji

“…Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer…”
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SPARSE PCA: OPTIMAL RATES AND ADAPTIVE ESTIMATION by Cai, T. Tony, Ma, Zongming, Wu, Yihong

“…Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax…”
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Two‐sample test of high dimensional means under dependence by Tony Cai, T, Liu, Weidong, Xia, Yin

“…The paper considers in the high dimensional setting a canonical testing problem in multivariate analysis, namely testing the equality of two mean vectors. We…”
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The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy by Cai, T. Tony, Wang, Yichen, Zhang, Linjun

“…Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the…”
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Semisupervised inference for explained variance in high dimensional linear regression and its applications by Tony Cai, T., Guo, Zijian

“…Summary The paper considers statistical inference for the explained variance βTΣβ under the high dimensional linear model Y=Xβ+ε in the semisupervised setting,…”
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LIMITING LAWS OF COHERENCE OF RANDOM MATRICES WITH APPLICATIONS TO TESTING COVARIANCE STRUCTURE AND CONSTRUCTION OF COMPRESSED SENSING MATRICES by Cai, T. Tony, Jiang, Tiefeng

“…Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important…”
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Minimax and Adaptive Prediction for Functional Linear Regression by Cai, T. Tony, Yuan, Ming

“…This article considers minimax and adaptive prediction with functional predictors in the framework of functional linear model and reproducing kernel Hilbert…”
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Transfer learning for high‐dimensional linear regression: Prediction, estimation and minimax optimality by Li, Sai, Cai, T. Tony, Li, Hongzhe

“…This paper considers estimation and prediction of a high‐dimensional linear regression in the setting of transfer learning where, in addition to observations…”
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Transfer Learning in Large-Scale Gaussian Graphical Models with False Discovery Rate Control by Li, Sai, Cai, T. Tony, Li, Hongzhe

“…Transfer learning for high-dimensional Gaussian graphical models (GGMs) is studied. The target GGM is estimated by incorporating the data from similar and…”
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LIMITING LAWS FOR DIVERGENT SPIKED EIGENVALUES AND LARGEST NONSPIKED EIGENVALUE OF SAMPLE COVARIANCE MATRICES by Cai, T. Tony, Han, Xiao, Pan, Guangming

“…We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance…”
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Prediction in Functional Linear Regression by Cai, T. Tony, Hall, Peter

“…There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case…”
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High dimensional linear discriminant analysis: optimality, adaptive algorithm and missing data by Cai, T. Tony, Zhang, Linjun

“…The paper develops optimality theory for linear discriminant analysis in the high dimensional setting. A data-driven and tuning-free classification rule, which…”
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Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-Rank Matrices by Cai, T. Tony, Anru Zhang

“…This paper considers compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for…”
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Optimal Permutation Recovery in Permuted Monotone Matrix Model by Ma, Rong, Tony Cai, T., Li, Hongzhe

“…Motivated by recent research on quantifying bacterial growth dynamics based on genome assemblies, we consider a permuted monotone matrix model , where the rows…”
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Confidence intervals for causal effects with invalid instruments by using two-stage hard thresholding with voting by Guo, Zijian, Kang, Hyunseung, Cai, T. Tony, Small, Dylan S.

“…A major challenge in instrumental variable (IV) analysis is to find instruments that are valid, or have no direct effect on the outcome and are ignorable…”
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Estimation and Inference for High-Dimensional Generalized Linear Models with Knowledge Transfer by Li, Sai, Zhang, Linjun, Cai, T. Tony, Li, Hongzhe

“…Transfer learning provides a powerful tool for incorporating data from related studies into a target study of interest. In epidemiology and medical studies,…”
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