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Topics:
- Statistical Machine Learning
- Transfer Learning
- Differentially Private Learning
- Federated Learning
- Interplay between Statistical Accuracy and Computational Costs
- Transfer Learning
- High-Dimensional Statistics
- PCA, SVD, & Inference for Low-Rank Matrices
- Inference for High-Dimensional Covariance Structures
- Compressed Sensing, High-Dimensional Linear Models & GLMs
- Supervised, Unsupervised, & Semi-Supervised Learning
- Network Data Analysis
- Detection & Identification of Sparse Signals
- Other Problems
- PCA, SVD, & Inference for Low-Rank Matrices
- Large-Scale Multiple Testing
- Functional Data Analysis
- Theory & Methodology for Nonparametric Function Estimation
- Inference for Linear, Quadratic, & Nonsmooth Functionals
- Uncertainty Quantification
- Inference for Discrete Distributions
- Applications to Genomics, Chemical Identification, & Medical Imaging
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Statistical Machine Learning
- Cai, T. T. & Kim, D. (2024).
Transfer learning for covariance matrix estimation: Optimality and adaptivity.
Technical report. - Auddy, A., Cai, T. T., & Chakraborty, A. (2024).
Minimax and adaptive transfer learning for nonparametric classification under distributed differential privacy constraints.
Technical report. - Cai, T.T. & Pu, H. (2022).
Transfer learning for nonparametric regression: Non-asymptotic minimax analysis and adaptive procedure.
Technical report. - Li, S., Zhang, L., Cai, T.T., & Li, H. (2024).
Estimation and inference for high-dimensional generalized linear models with knowledge transfer.
Journal of the American Statistical Association 119, 1274-1285. - Cai, T.T., Kim, D., & Pu, H. (2024).
Transfer learning for functional mean estimation: Phase transition and adaptive algorithms.
The Annals of Statistics 52, 654-678. - Cai, C., Cai, T.T., & Li, H. (2024).
Transfer learning for contextual multi-armed bandits.
The Annals of Statistics 52, 207-232. - Li, S., Cai, T. T., & Li, H. (2023).
Transfer learning in large-scale Gaussian graphical models with false discovery rate control.
Journal of the American Statistical Association 118, 2171-2183. - Li, S., Cai, T. T., & Li, H. (2022).
Transfer learning for high-dimensional linear regression: Prediction, estimation, and minimax optimality.
Journal of the Royal Statistical Society, Series B 84, 149-173. - Cai, T. T. & Wei, H. (2021).
Transfer learning for nonparametric classification: Minimax rate and adaptive classifier.
The Annals of Statistics 49, 100-128. - Auddy, A., Cai, T. T., & Chakraborty, A. (2024).
Minimax and adaptive transfer learning for nonparametric classification under distributed differential privacy constraints.
Technical report. - Cai, T. T., Chakraborty, A., & Vuursteen, L. (2024).
Federated nonparametric hypothesis testing with differential privacy constraints: Optimal rates and adaptive tests.
Technical report. - Cai, T. T., Xia, D., & Zha, M. (2024).
Optimal differentially private PCA and estimation for spiked covariance matrices.
Technical report. - Cai, T. T., Chakraborty, A., & Vuursteen, L. (2023).
Optimal federated learning for nonparametric regression with heterogenous distributed differential privacy constraints.
Technical report. - Cai, T. T., Wang, Y., & Zhang, L. (2023).
Score attack: A lower bound technique for optimal differentially private learning.
Technical report. - Cai, T. T., Wang, Y., & Zhang, L. (2021).
The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy.
The Annals of Statistics 49, 2825-2850. - Cai, T. T., Chakraborty, A., & Vuursteen, L. (2024).
Federated nonparametric hypothesis testing with differential privacy constraints: Optimal rates and adaptive tests.
Technical report. - Cai, T. T., Chakraborty, A., & Vuursteen, L. (2023).
Optimal federated learning for nonparametric regression with heterogenous distributed differential privacy constraints.
Technical report. - Cai, T. T. & Wei, H. (2024).
Distributed Gaussian mean estimation under communication constraints: Optimal rates and communication-efficient algorithms.
Journal of Machine Learning Research 25, 1-63. - Cai, T. T. & Wei, H. (2022).
Distributed adaptive Gaussian mean estimation with unknown variance: Interactive protocols help adaptation.
The Annals of Statistics 50, 1992-2020. - Cai, T. T. & Wei, H. (2022).
Distributed nonparametric regression: Optimal rate of convergence and cost of adaptation.
The Annals of Statistics, 50, 698-725.Interplay between Statistical Accuracy and Computational Costs
- Cai, T. T. & Wu, Y. (2020).
Statistical and computational limits for sparse matrix detection.
The Annals of Statistics 48, 1593-1614. - Cai, T. T., Liang, T., & Rakhlin, A. (2017).
Computational and statistical boundaries for submatrix localization in a large noisy matrix.
The Annals of Statistics 45, 1403-1430.PCA, SVD, & Inference for High-Dimensional Low-Rank Matrices
- Cai, T. T., Xia, D., & Zha, M. (2024).
Optimal differentially private PCA and estimation for spiked covariance matrices.
Technical report. - Cai, T. T., Li, H., & Ma, R. (2021).
Optimal structured principal subspace estimation: Metric entropy and minimax rates.
Journal of Machine Learning Research 22, 1-45. - Cai, T. T., Han, X., & Pan, G. (2020).
Limiting laws for divergent spiked eigenvalues and largest non-spiked eigenvalue of sample covariance matrices.
The Annals of Statistics 48, 1255-1280. - Zhang, A., Cai, T. T., & Wu, Y. (2022).
Heteroskedastic PCA: Algorithm, optimality, and applications.
The Annals of Statistics 50, 53-80. - Cai, T. T. & Zhang, A. (2018).
Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics.
The Annals of Statistics, 46, 60-89. - Cai, T. T., Li, X., & Ma, Z. (2016).
Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow.
The Annals of Statistics 44, 2221-2251. - Cai, T. T. & Zhou, W. (2016).
Matrix completion via max-norm constrained optimization.
Electronic Journal of Statistics 10, 1493-1525. - Cai, T., Cai, T. T., & Zhang, A. (2016).
Structured matrix completion with applications to genomic data integration.
Journal of the American Statistical Association 111, 621-633. - Cai, T. T., Liang, T., & Rakhlin, A. (2016).
Geometric inference for general high-dimensional linear inverse problems.
The Annals of Statistics 44, 1536–1563. - Cai, T. T., Ma, Z., & Wu, Y. (2015).
Optimal estimation and rank detection for sparse spiked covariance matrices.
Probability Theory and Related Fields 161, 781-815. - Cai, T. T. & Zhang, A. (2015).
ROP: Matrix recovery via rank-one projections.
The Annals of Statistics 43, 102-138. - Cai, T. T. & Zhang, A. (2014).
Sparse representation of a polytope and recovery of sparse signals and low-rank matrices.
IEEE Transactions on Information Theory 60, 122-132. - Cai, T. T., Ma, Z., & Wu, Y. (2013).
Sparse PCA: Optimal rates and adaptive estimation.
The Annals of Statistics 41, 3074-3110. - Cai, T. T. & Zhou, W. (2013).
A max-norm constrained minimization approach to 1-bit matrix completion.
Journal of Machine Learning Research 14, 3619-3647. - Cai, T. T. & Zhang, A. (2013).
Compressed sensing and affine rank minimization under restricted isometry.
IEEE Transactions on Signal Processing 61, 3279-3290. - Cai, T. T. & Zhang, A. (2013).
Sharp RIP bound for sparse signal and low-rank matrix recovery.
Applied And Computational Harmonic Analysis 35, 74-93. - Cai, T. T. & Kim, D. (2024).
Transfer Learning for Covariance Matrix Estimation: Optimality and Adaptivity.
Technical report. - Cai, T. T., Li, H., & Ma, R. (2021).
Optimal structured principal subspace estimation: Metric entropy and minimax rates.
Journal of Machine Learning Research 22, 1-45. - Zhang, A., Cai, T. T., & Wu, Y. (2022).
Heteroskedastic PCA: Algorithm, optimality, and applications.
The Annals of Statistics 50, 53-80. - Cai, T. T., Han, X., & Pan, G. (2020).
Limiting laws for divergent spiked eigenvalues and largest non-spiked eigenvalue of sample covariance matrices.
The Annals of Statistics 48, 1255-1280. - Cai, T. T., Hu, J., Li, Y., & Zheng, X. (2020).
High-dimensional minimum variance portfolio estimation based on high-frequency data.
The Journal of Econometrics 214, 482-494. - Cai, T. T. & Zhang, A. (2018).
Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics.
The Annals of Statistics 46, 60-89. - Xia, Y., Cai, T., & Cai, T. T. (2018).
Multiple testing of submatrices of a precision matrix with applications to identification of between pathway interactions.
Journal of the American Statistical Association 113, 328-339. - Cai, T. T. & Zhang, A. (2016).
Minimax rate-optimal estimation of high-dimensional covariance matrices with incomplete data.
Journal of Multivariate Analysis 150, 55-74. - Cai, T. T. & Yuan, M. (2016).
Minimax and adaptive estimation of covariance operator for random variables observed on a lattice graph.
Journal of the American Statistical Association 111, 253-265. - Cai, T. T. & Liu, W. (2016).
Large-scale multiple testing of correlations.
Journal of the American Statistical Association 111, 229-240. - Cai, T. T., Ren, Z., & Zhou, H. (2016).
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (with discussion).
Electronic Journal of Statistics 10, 1-59.
(Rejoinder) - Cai, T. T. & Zhang, A. (2016).
Inference for high-dimensional differential correlation matrices.
Journal of Multivariate Analysis 143, 107–126. - Cai, T. T., Li, H., Liu, W., & Xie, J. (2016).
Joint estimation of multiple high-dimensional precision matrices.
Statistica Sinica 26, 445-464. - Cai, T. T., Liu, W., & Zhou, H. (2016).
Estimating sparse precision matrix: Optimal rates of convergence and adaptive estimation.
The Annals of Statistics 44, 455-488. - Xia, Y., Cai, T., & Cai, T. T. (2015).
Testing differential networks with applications to detecting gene-by-gene interactions.
Biometrika 102, 247-266. - Cai, T. T., Liang, T., & Zhou, H. (2015).
Law of log determinant of sample covariance matrix and optimal estimation of differential entropy for high-dimensional Gaussian distributions.
Journal of Multivariate Analysis 137, 161-172. - Cai, T. T., Ma, Z., & Wu, Y. (2015).
Optimal estimation and rank detection for sparse spiked covariance matrices.
Probability Theory and Related Fields 161, 781-815. - Zhao, S.D., Cai, T. T., & Li, H. (2014).
Direct estimation of differential networks.
Biometrika 101, 253-268. - Cai, T. T., Ma, Z., & Wu, Y. (2013).
Sparse PCA: Optimal rates and adaptive estimation.
The Annals of Statistics 41, 3074-3110. - Cai, T. T. & Ma, Z. (2013).
Optimal hypothesis testing for high dimensional covariance matrices.
Bernoulli 19, 2359-2388. - Cai, T. T., Ren, Z., & Zhou, H. (2013).
Optimal rates of convergence for estimating Toeplitz covariance matrices.
Probability Theory and Related Fields 156, 101-143. - Cai, T. T., Liu, W., & Xia, Y. (2013).
Two-sample covariance matrix testing and support recovery in high-dimensional and sparse settings.
Journal of the American Statistical Association 108, 265-277. - Cai, T. T., Li, H., Liu, W., & Xie, J. (2013).
Covariate adjusted precision matrix estimation with an application in genetical genomics.
Biometrika 100, 139-156. - Cai, T. T. & Zhou, H. (2012).
Optimal rates of convergence for sparse covariance matrix estimation.
The Annals of Statistics 40, 2389-2420. - Cai, T. T. & Zhou, H. (2012).
Minimax estimation of large covariance matrices under l1 norm (with discussion).
Statistica Sinica 22, 1319-1378. - Cai, T. T. & Yuan, M. (2012).
Adaptive covariance matrix estimation through block thresholding.
The Annals of Statistics 40, 2014-2042. - Cai, T. T. & Jiang, T. (2012).
Phase transition in limiting distributions of coherence of high-dimensional random matrices.
Journal of Multivariate Analysis 107, 24-39. - Cai, T. T. & Liu, W. (2011).
Adaptive thresholding for sparse covariance matrix estimation.
Journal of the American Statistical Association 106, 672-684. - Cai, T. T., Liu, W., & Luo, X. (2011).
A constrained l1 minimization approach to sparse precision matrix estimation.
Journal of the American Statistical Association 106, 594-607. - Cai, T. T. & Jiang, T. (2011).
Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices.
The Annals of Statistics 39, 1496-1525. - Cai, T. T., Zhang, C.-H., & Zhou, H. (2010).
Optimal rates of convergence for covariance matrix estimation.
The Annals of Statistics 38, 2118-2144. - Zhang, L., Ma, R., Cai, T. T., & Li, H. (2024).
Estimation, confidence intervals, and large-scale multiple testing for high-dimensional mixed linear regression.
Technical report. - Cai, T. T., Wang, Y., & Zhang, L. (2023).
Score attack: A lower bound technique for optimal differentially private learning.
Technical report. - Rakshit, R., Wang, Z., Cai, T. T., & Guo, Z.(2024+).
SIHR: Statistical inference in high-dimensional linear and logistic regression models.
The R Journal, to appear. - Li, S., Cai, T.T., & Li, H. (2024+).
Statistical inference for high dimensional regression with proxy data.
Statistica Sinica, to appear. - Ma, R., Guo, Z., Cai, T. T., & Li, H. (2024).
Statistical inference for genetic relatedness based on high-dimensional logistic regression.
Statistica Sinica 34, 1023-1043. - Cai, T. T., Guo, Z., & Xia, Y. (2023).
Statistical inference and large-scale multiple testing for high-dimensional regression models (with discussion).
Test 32, 1135-1171. - Cai, T. T., Guo, Z., & Ma, R. (2023).
Statistical inference for high-dimensional generalized linear models with binary outcomes.
Journal of the American Statistical Association 118, 1319-1332. - Cai, T., Cai, T. T., & Guo, Z. (2021).
Optimal statistical inference for individualized treatment effects in high-dimensional models.
Journal of the Royal Statistical Society, Series B 83, 669-719. - Cai, T. T., Zhang, A., & Zhou, Y. (2022).
Sparse group Lasso: Sample complexity, optimal rate, and statistical inference.
IEEE Transactions on Information Theory 68, 5975-6002. - Chakrabortty, A., Lu, J., Cai, T. T., & Li, H. (2019).
High dimensional M-estimation with missing outcomes: A semi-parametric framework.
Technical report. - Li, S., Cai, T. T., & Li, H. (2022).
Inference for high-dimensional linear mixed-effects models: A quasi-likelihood approach.
Journal of the American Statistical Association 117, 1835-1846. - Kang, H., Lee, Y., Cai, T. T., & Small, D. (2022).
Two robust tools for inference about causal effects with invalid instruments.
Biometrics 78, 24-34. - Cai, T. T., Wang, Y., & Zhang, L. (2021).
The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy.
The Annals of Statistics 49, 2825-2850. - Guo, Z., Renaux, C., Buhlmann, P., & Cai, T. T. (2021).
Group inference in high dimensions with applications to hierarchical testing.
Electronic Journal of Statistics 15, 6633-6676. - Cai, T. T. & Guo, Z. (2020).
Semi-supervised inference for explained variance in high-dimensional regression and its applications.
Journal of the Royal Statistical Society, Series B 82, 391-419. - Guo, Z., Wang, W., Cai, T. T., & Li, H. (2019).
Optimal estimation of genetic relatedness in high-dimensional linear models.
Journal of the American Statistical Association 114, 358-369. - Guo, Z., Kang, H., Cai, T. T., & Small, D. (2018).
Testing endogeneity with high dimensional covariates.
The Journal of Econometrics 207, 175-187. - Guo, Z., Kang, H., Cai, T. T., & Small, D. (2018).
Confidence intervals for causal effects with invalid instruments using two-stage hard thresholding with voting.
Journal of the Royal Statistical Society, Series B 80, 793-815. - Cai, T. T. & Guo, Z. (2018).
Accuracy assessment for high-dimensional linear regression.
The Annals of Statistics 46, 1807-1836. - Xia, Y., Cai, T., & Cai, T. T. (2018).
Two-sample tests for high-dimensional linear regression with an application to detecting interactions.
Statistica Sinica 28, 63-92. - Cai, T. T. & Guo, Z. (2017).
Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity.
The Annals of Statistics 45, 615-646. - Cai, T. T., Liang, T., & Rakhlin, A. (2016).
Geometric inference for general high-dimensional linear inverse problems.
The Annals of Statistics 44, 1536–1563. - Kang, H., Zhang, A., Cai, T. T., & Small, D. (2016).
Instrumental variables estimation with some invalid instruments and its application to Mendelian randomization.
Journal of the American Statistical Association 111, 132-144. - Zhao, S.D., Cai, T. T., & Li, H. (2014).
More powerful genetic association testing via a new statistical framework for integrative genomics.
Biometrics 70, 881-890. - Cai, T. T. & Yuan, M. (2014).
Discussion: "A Significant Test for Lasso".
The Annals of Statistics 42, 478-482. - Cai, T. T. & Zhang, A. (2013).
Compressed sensing and affine rank minimization under restricted isometry.
IEEE Transactions on Signal Processing 61, 3279-3290. - Cai, T. T. & Zhang, A. (2013).
Sharp RIP bound for sparse signal and low-rank matrix recovery.
Applied And Computational Harmonic Analysis 35, 74-93. - Cai, T. T. & Wang, L. (2011).
Orthogonal matching pursuit for sparse signal recovery with noise.
IEEE Transactions on Information Theory 57, 4680-4688. - Cai, T. T. & Jiang, T. (2011).
Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices.
The Annals of Statistics 39, 1496-1525. - Cai, T. T., Wang, L., & Xu, G. (2010).
Stable recovery of sparse signals and an oracle inequality.
IEEE Transactions on Information Theory 56, 3516-3522. - Cai, T. T., Wang, L., & Xu, G. (2010).
Shifting inequality and recovery of sparse signals.
IEEE Transactions on Signal Processing 58, 1300-1308. - Cai, T. T., Xu, G., & Zhang, J. (2009).
On recovery of sparse signals via l1 minimization.
IEEE Transactions on Information Theory 55, 3388-3397. - Cai, T. T. & Lv, J. (2007).
Discussion of "The Dantzig Selector: Statistical estimation when p is much larger than n" by E. Candes and T. Tao.
The Annals of Statistics 35, 2365-2369. - Wu, R., Zhang, L., & Cai, T. T. (2023).
Supervised topic modeling: Optimal estimation and statistical inference.
Technical report. - Wu, R., Zhang, L., & Cai, T. T. (2023).
Sparse topic modeling: Computational efficiency, near-optimal algorithms, and statistical inference.
Journal of the American Statistical Association 118, 1849-1861. - Cai, T. T. & Zhang, L. (2021).
A convex optimization approach to high-dimensional sparse quadratic discriminant analysis.
The Annals of Statistics 49, 1537-1568. - Cai, T. T., Ma, J., & Zhang, L. (2019).
CHIME: Clustering of high-dimensional Gaussian mixtures with EM algorithm and its optimality.
The Annals of Statistics 47, 1234-1267. - Cai, T. T. & Zhang, L. (2019).
High-dimensional linear discriminant analysis: Optimality, adaptive algorithm, and missing data.
Journal of the Royal Statistical Society, Series B 81, 675-705. - Zhang, A., Brown, L. D., & Cai, T. T. (2019).
Semi-supervised inference: General theory and estimation of means.
The Annals of Statistics, 47, 2538-2566. - Cai, T. T. & Zhang, L. (2016).
Discussion of "Influential Feature PCA for High Dimensional Clustering".
The Annals of Statistics 44, 2372-2381. - Cai, T. T. & Liu, W. (2011).
A direct estimation approach to sparse linear discriminant analysis.
Journal of the American Statistical Association 106, 1566-1577. - Cai, T. T., Liang, T., & Rakhlin, A. (2020).
Weighted message passing and minimum energy flow for heterogeneous stochastic block models with side information.
Journal of Machine Learning Research 21, 1-34. - Cai, T. T., Liang, T., & Rakhlin, A. (2017).
On detection and structural reconstruction of small world random networks.
IEEE Transactions on Network Science and Engineering 4, 165-176. - Cai, T. T. & Li, X. (2015).
Robust and computationally feasible community detection in the presence of arbitrary outlier nodes.
The Annals of Statistics 43, 1027-1059. - Cai, T. T. & Wu, Y. (2020).
Statistical and computational limits for sparse matrix detection.
The Annals of Statistics 48, 1593-1614. - Zhao, S.D., Cai, T. T., & Li, H. (2017).
Optimal detection of weak positive latent dependence between two sequences of multiple tests.
Journal of Multivariate Analysis 160, 169–184. - Zhao, S.D., Cai, T. T., Cappola, T.P., Margulies, K.B., & Li, H. (2017).
Sparse simultaneous signal detection for identifying genetically controlled disease genes.
Journal of the American Statistical Association 112, 1032-1046. - Cai, T. T., Liang, T., & Rakhlin, A. (2017).
Computational and statistical boundaries for submatrix localization in a large noisy matrix.
The Annals of Statistics 45, 1403-1430. - Cai, T. T. & Sun, W. (2017).
Optimal screening and discovery of sparse signals with applications to multistage high-throughput studies.
Journal of the Royal Statistical Society, Series B 79, 197–223. - Jeng, J., Cai, T. T., & Li, H. (2015).
Sparse segment identifications with applications to DNA copy number variation analysis.
In Advanced Medical Statistics , 2nd Edition, Y. Lu, J. Fang, L., Tian, and H. Jin, eds., World Scientific, New Jersey, 863-887. - Cai, T. T. & Xia, Y. (2014).
High-Dimensional Sparse MANOVA.
Journal of Multivariate Analysis 131, 174-196. - Cai, T. T. & Yuan, M. (2014).
Rate-optimal detection of very short signal segments.
Technical report. - Cai, T. T. & Wu, Y. (2014).
Optimal detection for sparse mixtures against a given null distribution.
IEEE Transactions on Information Theory 60, 2217-2232. - Cai, T. T., Liu, W., & Xia, Y. (2014).
Two-sample test of high dimensional means under dependence.
Journal of the Royal Statistical Society, Series B 76, 349-372. - Jeng, J., Cai, T. T., & Li, H. (2013).
Simultaneous discovery of rare and common segment variants.
Biometrika 100, 157-172. - Cai, T. T., Jeng, J., & Li, H. (2012).
Robust detection and identification of sparse segments in ultra-high dimensional data analysis.
Journal of the Royal Statistical Society, Series B 74, 773-797. - Cai, T. T., Jeng, J., & Jin, J. (2011).
Optimal detection of heterogeneous and heteroscedastic mixtures.
Journal of the Royal Statistical Society, Series B 73, 629-662. - Xie, J., Cai, T. T., & Li, H. (2010).
Sample size and power analysis for sparse signal recovery in genome-wide association studies.
Biometrika 98, 273-290. - Jeng, J., Cai, T. T., & Li, H. (2010).
Optimal sparse segment identification with application in copy number variation analysis.
Journal of the American Statistical Association 105, 1156-1166. - Cai, T. T. Jin, J., & Low, M. (2007).
Estimation and confidence sets for sparse normal mixtures.
The Annals of Statistics 35, 2421-2449. - Auddy, A., Cai, T. T., & Li, H. (2024).
Regressing multivariate Gaussian distribution on vector covariates for co-expression network analysis.
Technical report. - Wang, S., Yuan, B., Cai, T. T., & Li, H. (2024).
Phylogenetic association analysis with conditional rank correlation.
Biometrika 111, 881-902. - Cai, T. T., Ke, Z. T., & Turner, P. (2024).
Testing high-dimensional multinomials with applications to text analysis.
Journal of the Royal Statistical Society, Series B 86, 922-942. - Cai, T.T. & Ma, R. (2024).
Matrix reordering for noisy disordered matrices: Optimality and computationally-efficient algorithms.
IEEE Transactions on Information Theory 70, 509-531. - Cai, T.T. & Ma, R. (2022).
Theoretical foundations of t-SNE for visualizing high-dimensional clustered data.
Journal of Machine Learning Research 23, 1-54. - Cai, T. T. Han, R., & Zhang, A. (2022).
On the non-asymptotic concentration of heteroskedastic wishart-type matrix.
Electronic Journal of Probability 27, 1-40. - Ma, R., Cai, T. T., & Li, H. (2022).
Optimal estimation of simultaneous signals using absolute inner product with applications to integrative genomics.
Statistica Sinica 32, 1027-1048. - Ma, R., Cai, T. T., & Li, H. (2021).
Optimal estimation of bacterial growth rates based on permuted monotone matrix.
Biometrika 108, 693–708. - Cai, T. T., Jiang, T., & Li, X. (2021).
Asymptotic analysis for extreme eigenvalues of principal minors of random matrices.
The Annals of Applied Probability 31, 2953-2990. - Ma, R., Cai, T. T., & Li, H. (2021).
Optimal permutation recovery in permuted monotone matrix model.
Journal of the American Statistical Association 116, 1358-1372. - Wang, S., Cai, T. T., & Li, H. (2021).
Optimal estimation of Wasserstein distance on a tree with an application to microbiome studies.
Journal of the American Statistical Association 116, 1237-1253. - Wang, S., Cai, T. T., & Li, H. (2021).
Hypothesis testing for phylogenetic composition: A minimum-cost flow perspective.
Biometrika 108, 17-36. - Cai, T. T., Kim, D., Song, X., & Wang, Y. (2021).
Optimal estimation of eigenspace of large density matrices of quantum systems based on Pauli measurements.
Journal of Statistical Planning and Inference 213, 50-71. - Cai, T. T. & Zhang, A. (2018).
Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics.
The Annals of Statistics 46, 60-89. - Cai, T. T. & Zhang, L. (2018).
High-dimensional Gaussian copula regression: Adaptive estimation and statistical inference.
Statistica Sinica 28, 963-993. - Cai, T. T., Liang, T., & Rakhlin, A. (2017).
Computational and statistical boundaries for submatrix localization in a large noisy matrix.
The Annals of Statistics 45, 1403-1430. - Cai, T. T., Li, X., & Ma, Z. (2016).
Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow.
The Annals of Statistics 44, 2221-2251. - Cai, T. T., Kim, D., Wang, Y., Yuan, M., & Zhou, H. (2016).
Optimal large-scale quantum state tomography with Pauli measurements.
The Annals of Statistics 44, 681-712. - Cai, T. T., Eldar, Y. C., & Li, X. (2016).
Global testing against sparse alternatives in time-frequency analysis.
The Annals of Statistics 44, 1438–1466. - Cai, T. T., Liang, T., & Rakhlin, A. (2016).
Geometric inference for general high-dimensional linear inverse problems.
The Annals of Statistics 44, 1536–1563. - Cai, T. T. & Xia, Y. (2014).
High-Dimensional Sparse MANOVA.
Journal of Multivariate Analysis 131, 174-196. - Cai, T. T., Liu, W., & Xia, Y. (2014).
Two-sample test of high dimensional means under dependence.
Journal of the Royal Statistical Society, Series B 76, 349-372. - Cai, T. T., Fan, J., & Jiang, T. (2013).
Distributions of angles in random packing on spheres.
Journal of Machine Learning Research 14, 1837-1864. - Cai, T. T. & Jiang, T. (2012).
Phase transition in limiting distributions of coherence of high-dimensional random matrices.
Journal of Multivariate Analysis 107, 24-39. - Cai, T. T. & Jiang, T. (2011).
Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices.
The Annals of Statistics 39, 1496-1525. - Xia, Y. & Cai, T. T. (2023).
Discussion of "A Scale-Free Approach for False Discovery Rate Control in Generalized Linear Models" by Dai, Lin, Xing, and Liu
Journal of the American Statistical Association 118, 1569-1572. - Liang, Z., Cai, T.T., Sun, W., & Xia, Y. (2024+).
A locally adaptive algorithm for multiple testing with network structure.
Statistica Sinica, to appear. - Cai, T. T., Sun, W., & Xia, Y. (2022).
LAWS: A locally adaptive weighting and screening approach to spatial multiple testing.
Journal of the American Statistical Association 117, 1370-1383. - Ma, R., Cai, T. T., & Li, H. (2021).
Global and simultaneous testing for high-dimensional logistic regression models.
Journal of the American Statistical Association 116, 984-998. - Xia, Y., Cai, T. T., & Sun, W. (2020).
GAP: A general framework for information pooling in two-sample sparse inference.
Journal of the American Statistical Association 115, 1236-1250. - Cai, T. T., Li, H., Ma, J., & Xia, Y. (2019).
Differential Markov random field analysis with an application to detecting differential microbial community networks.
Biometrika 106, 401-416. - Xiang, D., Zhao, S. D., & Cai, T. T. (2019).
Signal classification for the integrative analysis of multiple sequences of multiple tests.
Journal of the Royal Statistical Society, Series B 81, 707-734. - Cai, T. T., Sun, W., & Wang, W. (2019).
CARS: Covariate assisted ranking and screening for large-scale two-sample inference (with discussion).
Journal of the Royal Statistical Society, Series B 81, 187-234. - Cai, T., Cai, T. T., Liao, K., & Liu, W. (2019).
Large-scale simultaneous testing of cross-covariance matrix with applications to PheWAS.
Statistica Sinica 29, 983-1005. - Basu, P., Cai, T. T., Das, K., & Sun, W. (2018).
Weighted false discovery rate control in large-scale multiple testing.
Journal of the American Statistical Association 113, 1172-1183. - Xia, Y., Cai, T. T. & Li, H. (2018).
Joint testing and false discovery rate control for high-dimensional multivariate regression.
Biometrika 105, 249-269. - Xia, Y., Cai, T., & Cai, T. T. (2018).
Multiple testing of submatrices of a precision matrix with applications to identification of between pathway interactions.
Journal of the American Statistical Association 113, 328-339. - Xia, Y., Cai, T., & Cai, T. T. (2018).
Two-sample tests for high-dimensional linear regression with an application to detecting interactions.
Statistica Sinica 28, 63-92. - Cai, T. T. & Sun, W. (2017).
Large-scale global and simultaneous inference: Estimation and testing in very high dimensions.
Annual Review of Economics 9, 411-439. - Cai, T. T. (2017).
Global testing and large-scale multiple testing for high-dimensional covariance structures.
Annual Review of Statistics and Its Applications 4, 423–446. - Cai, T. T. & Liu, W. (2016).
Large-scale multiple testing of correlations.
Journal of the American Statistical Association111, 229-240. - Xia, Y., Cai, T., & Cai, T. T. (2015).
Testing differential networks with applications to detecting gene-by-gene interactions.
Biometrika 102, 247-266. - Sun, W., Reich, B. J., Cai, T. T., Guindani, M., & Schwartzman, A. (2015).
False discovery control in large-scale spatial multiple testing.
Journal of the Royal Statistical Society, Series B 77, 59-83. - Xie, J., Cai, T. T., Maris, J. & Li, H. (2011).
Optimal false discovery rate control for dependent data.
Statistics and Its Interface 4, 417-430. - Cai, T. T. & Sun, W. (2011).
A compound decision-theoretic approach to large-scale multiple testing.
In High-dimensional Data Analysis, pages 75–116. World Scientific. - Cai, T. T. & Jin, J. (2010).
Optimal rates of convergence for estimating the null and proportion of non-null effects in large-scale multiple testing.
The Annals of Statistics 38, 100-145. - Cai, T. T. & Sun, W. (2010).
A compound decision-theoretic approach to large-scale multiple testing.
In High-Dimensional Data Analysis , T. T. Cai and X. Shen, eds., World Scientific, New Jersey, 75-116. - Cai, T. T. (2010).
Comments on "Correlated z-values and the Accuracy of Large-Scale Statistical Estimates" by Bradley Efron.
Journal of the American Statistical Association 105, 1055-1056. - Cai, T. T. & Sun, W. (2009).
Simultaneous testing of grouped hypotheses: Finding needles in multiple haystacks.
Journal of the American Statistical Association 104, 1467 - 1481. - Sun, W. & Cai, T. T. (2009).
Large-scale multiple testing under dependency.
Journal of the Royal Statistical Society, Series B 71, 393-424. - Sun, W. & Cai, T. T. (2007).
Oracle and adaptive compound decision rules for false discovery rate control.
Journal of the American Statistical Association 102, 901-912. - Jin, J. & Cai, T. T. (2007).
Estimating the null and the proportion of non-null effects in large-scale multiple comparisons.
Journal of the American Statistical Association 102, 495-506. - Cai, T. T. (2008).
Discussion of "Microarrays, Empirical Bayes, and the Two-Group Model" by Bradley Efron.
Statistical Science 23, 29-33. - Cai, T.T., Kim, D., & Pu, H. (2023).
Transfer learning for functional mean estimation: Phase transition and adaptive algorithms.
Technical report. - Cai, T. T., Zhang, L., & Zhou, H. H. (2018).
Adaptive functional linear regression via functional principal component analysis and block thresholding.
Statistica Sinica 28, 2455-2468. - Cai, T. T. & Yuan, M. (2012).
Minimax and adaptive prediction for functional linear regression.
Journal of the American Statistical Association 107, 1201-1216. - Cai, T. T. & Yuan, M. (2011).
Optimal estimation of the mean function based on discretely sampled functional data: Phase transition.
The Annals of Statistics 39, 2330-2355. - Cai, T. T. & Yuan, M. (2010).
Nonparametric covariance function estimation for functional and longitudinal data.
Technical Report. - Yuan, M. & Cai, T. T. (2010).
A reproducing kernel Hilbert space approach to functional linear regression.
The Annals of Statistics 38, 3412-3444. - Cai, T. T. & Hall, P. (2006).
Prediction in functional linear regression.
The Annals of Statistics 34, 2159-2179. - Cai, T.T., Chen, R., & Zhu, Y. (2024).
Estimation and inference for minimizer and minimum of convex functions: Optimality, adaptivity, and uncertainty principles.
The Annals of Statistics 52, 392-411. - Cai, T.T. & Pu, H. (2022).
Stochastic continuum-armed bandits with additive models: Minimax regrets and adaptive algorithm.
The Annals of Statistics 50, 2179-2204. - Cai, T. T. & Wei, H. (2021).
Transfer learning for nonparametric classification: Minimax rate and adaptive classifier.
The Annals of Statistics 49, 100-128. - Cai, T. T. (2019).
Gaussianization Machines for non-Gaussian function estimation models.
Statistical Science 34, 635–656. - Cai, T. T., Guntuboyina, A., & Wei, Y. (2018).
Adaptive estimation of planar convex sets.
The Annals of Statistics 46, 1018-1049. - Cai, T. T. & Low, M. (2015).
A framework for estimation of convex functions.
Statistica Sinica 25, 423-456. - Cai, T. T., Low, M., & Ma, Z. (2014).
Adaptive confidence bands for nonparametric regression functions.
Journal of the American Statistical Association 109, 1054-1070. - Cai, T. T., Low, M., & Xia, Y. (2013).
Adaptive confidence intervals for regression functions under shape constraints.
The Annals of Statistics 41, 722-750. - Cai, T. T. (2012).
Minimax and adaptive inference in nonparametric function estimation.
Statistical Science 27, 31-50. - Wang, L., Brown, L.D., & Cai, T. T. (2011).
A difference based approach to the semiparametric partial linear model.
Electronic Journal of Statistics 5, 619-641. - Cai, T. T. & Zhou, H. (2010).
Nonparametric regression in natural exponential families.
In Borrowing Strength: Theory Powering Applications -- A Festschrift for Lawrence D. Brown, IMS Collections Vol. 6, 199-215. - Cai, T. T. & Zhou, H. (2009).
Asymptotic equivalence and adaptive estimation for robust nonparametric regression.
The Annals of Statistics 37, 3204-3235. - Cai, T. T. (2008).
On information pooling, adaptability and superefficiency in nonparametric function estimation.
Journal of Multivariate Analysis 99, 412-436. - Cai, T. T., Low, M., & Zhao, L. (2007).
Tradeoffs between global and local risks in nonparametric function estimation.
Bernoulli 13, 1-19. - Cai, T. T. & Hall, P. (2006).
Prediction in functional linear regression.
The Annals of Statistics 34, 2159-2179. - Cai, T. T. & Low, M. (2005).
Nonparametric function estimation over shrinking neighborhoods: Superefficiency and adaptation.
The Annals of Statistics 33, 184-213. - Cai, T. T. (2003).
Rates of convergence and adaptation over Besov spaces under pointwise risk.
Statistica Sinica 13, 881-902. - Brown, L.D., Cai, T. T., Low, M.G., & Zhang, C. (2002).
Asymptotic equivalence theory for nonparametric regression with random design.
The Annals of Statistics 30, 688-707. - Cai, T. T. & Zhou, H. (2010).
Nonparametric regression in natural exponential families.
In Borrowing Strength: Theory Powering Applications -- A Festschrift for Lawrence D. Brown, IMS Collections Vol. 6, 199-215. - Brown, L. D., Cai, T. T., & Zhou, H. (2010).
Nonparametric regression in exponential families.
The Annals of Statistics 38, 2005-2046. - Brown, L. D., Cai, T. T., Zhang, R., Zhao, L., & Zhou, H. (2010).
The root-unroot algorithm for density estimation as implemented via wavelet block thresholding.
Probability Theory and Related Fields 146, 401-433. - Cai, T. T. & Zhou, H. (2009).
Asymptotic equivalence and adaptive estimation for robust nonparametric regression.
The Annals of Statistics 37, 3204-3235. - Cai, T. T. & Zhou, H. (2009).
A data-driven block thresholding approach to wavelet estimation.
The Annals of Statistics 37, 569-595. - Cai, T. T., Low, M., & Zhao, L. (2009).
Sharp adaptive estimation by a blockwise method.
Journal of Nonparametric Statistics 21, 839-850. - Cai, T. T. & Wang, L. (2008).
Adaptive variance function estimation in heteroscedastic nonparametric regression.
The Annals of Statistics 36, 2025-2054. - Brown, L. D., Cai, T. T., & Zhou, H. (2008).
Robust nonparametric estimation via wavelet median regression.
The Annals of Statistics 36, 2055-2084. - Chicken, E. & Cai, T. T. (2005).
Block thresholding for density estimation: Local and global adaptivity.
Journal of Multivariate Analysis 95, 76-106. - Cai, T. T. (2003).
Rates of convergence and adaptation over Besov spaces under pointwise risk.
Statistica Sinica 13, 881-902. - Cai, T. T. (2002).
On adaptive wavelet estimation of a derivative and other related linear inverse problems.
J. Statistical Planning and Inference 108, 329-349. - Cai, T. T. (2002).
On block thresholding in wavelet regression: Adaptivity, block size, and threshold level.
Statistica Sinica 12, 1241-1273. - Cai, T. T. (2001).
Discussion on "regularization of wavelets approximations" by A. Antoniadis and J. Fan.
Journal of the American Statistical Association 96, 960-962. - Cai, T. T., Zhang, D., & Ben-Amotz, D. (2001).
Enhanced chemical classification of Raman images using wavelet transformation.
Applied Spectroscopy 55, 1124-1130. - Cai, T. T. & Silverman, B.W. (2001).
Incorporating information on neighboring coefficients into wavelet estimation.
Sankhya 63, 127-148. - Cai, T. T. (1999).
Adaptive wavelet estimation: a block thresholding and oracle inequality approach.
The Annals of Statistics 27, 898-924. - Cai, T. T. & Brown, L.D. (1999).
Wavelet estimation for samples with random uniform design.
Statistics and Probability Letters 42, 313-321. - Cai, T. T. & Brown, L.D. (1998).
Wavelet shrinkage for nonequispaced samples.
The Annals of Statistics 26, 1783-1799. - Cai, T. T., Munk, A., & Schmidt-Hieber, J. (2010).
Sharp minimax estimation of the variance of Brownian motion corrupted with Gaussian noise.
Statistica Sinica 20, 1011-1024. - Cai, T. T., Levine, M., & Wang, L. (2009).
Variance function estimation in multivariate nonparametric regression.
Journal of Multivariate Analysis 100, 126-136. - Cai, T. T. & Wang, L. (2008).
Adaptive variance function estimation in heteroscedastic nonparametric regression.
The Annals of Statistics 36, 2025-2054. - Wang, L., Brown, L. D., Cai, T. T., & Levine, M. (2008).
Effect of mean on variance function estimation in nonparametric regression.
The Annals of Statistics 36, 646-664.Inference for Linear, Quadratic, & Nonsmooth Functionals
- Cai, T. T. & Guo, Z. (2020).
Semi-supervised inference for explained variance in high-dimensional regression and its applications.
Journal of the Royal Statistical Society, Series B 82, 391-419. - Cai, T. T. & Guo, Z. (2018).
Accuracy assessment for high-dimensional linear regression.
The Annals of Statistics 46, 1807-1836. - Cai, T. T. & Guo, Z. (2017).
Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity.
The Annals of Statistics 45, 615-646. - Cai, T. T. & Tan, X. L. (2017).
Optimal estimation of a quadratic functional under the Gaussian two-sequence model.
Statistica Sinica 27, 879-906. - Cai, T. T., Low, M., & Ma, Z. (2014).
Adaptive confidence bands for nonparametric regression functions.
Journal of the American Statistical Association 109, 1054-1070. - Cai, T. T., Low, M., & Xia, Y. (2013).
Adaptive confidence intervals for regression functions under shape constraints.
The Annals of Statistics 41, 722-750. - Cai, T. T. (2012).
Minimax and adaptive inference in nonparametric function estimation.
Statistical Science 27, 31-50. - Cai, T. T. & Low, M. (2011).
Testing composite hypotheses, Hermite polynomials, & optimal estimation of a nonsmooth functional.
The Annals of Statistics 39, 1012-1041. - Cai, T. T. & Low, M. (2006).
Optimal adaptive estimation of a quadratic functional.
The Annals of Statistics 34, 2298-2325. - Cai, T. T. & Low, M. (2006).
Adaptive confidence balls.
The Annals of Statistics 34, 202-228. - Cai, T. T. & Low, M. (2006).
Adaptation under probabilistic error for estimating linear functionals.
Journal of Multivariate Analysis 97, 231-245. - Cai, T. T. & Low, M. (2005).
Non-quadratic estimators of a quadratic functional.
The Annals of Statistics 33, 2930-2956. - Cai, T. T. & Low, M. (2005).
On adaptive estimation of linear functionals.
The Annals of Statistics 33, 2311-2343. - Cai, T. T. & Low, M. (2005).
Adaptive estimation of linear functionals under different performance measures.
Bernoulli 11, 341-358. - Cai, T. T. & Low, M. (2004).
An adaptation theory for nonparametric confidence intervals.
The Annals of Statistics 32, 1805-1840. - Cai, T. T. & Low, M. (2004).
Minimax estimation of linear functionals over nonconvex parameter spaces.
The Annals of Statistics 32, 552 - 576. - Cai, T. T. & Low, M. (2003).
A note on nonparametric estimation of linear functionals.
The Annals of Statistics 31, 1140-1153. - Cai, T. T. & Low, M. (2002).
On modulus of continuity and adaptability in nonparametric functional estimation.
Technical Report. - Cai, T. T. & Guo, Z. (2018).
Accuracy assessment for high-dimensional linear regression.
The Annals of Statistics 46, 1807-1836. - Cai, T. T. & Guo, Z. (2017).
Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity.
The Annals of Statistics 45, 615-646. - Cai, T. T., Low, M., & Ma, Z. (2014).
Adaptive confidence bands for nonparametric regression functions.
Journal of the American Statistical Association 109, 1054-1070. - Cai, T. T., Low, M., & Xia, Y. (2013).
Adaptive confidence intervals for regression functions under shape constraints.
The Annals of Statistics 41, 722-750. - Cai, T. T. & Low, M. (2006).
Adaptive confidence balls.
The Annals of Statistics 34, 202-228. - Cai, T. T. & Low, M. (2004).
An adaptation theory for nonparametric confidence intervals.
The Annals of Statistics 32, 1805-1840. - Brown, L.D., Cai, T. T., & DasGupta, A. (2003).
Interval estimation in exponential families.
Statistica Sinica 13, 19-49. - Brown, L.D., Cai, T. T., & DasGupta, A. (2002).
Confidence intervals for a binomial proportion and asymptotic expansions.
The Annals of Statistics 30, 160-201. - Brown, L.D., Cai, T. T., & DasGupta, A. (2001).
Interval estimation for a binomial proportion (with discussion).
Statistical Science 16, 101-133.Inference for Discrete Distributions
- Cai, T. T. & Wang, H. (2009).
Tolerance intervals for discrete distributions in exponential families.
Statistica Sinica 19, 905-923. - Cai, T. T. (2005).
One-sided confidence intervals in discrete distributions.
J. Statistical Planning and Inference 131, 63-88. - Brown, L.D., Cai, T. T., & DasGupta, A. (2005).
Discussion of "fuzzy and randomized confidence intervals and p-values" by C. J. Geyer and G. D. Meeden.
Statistical Science 20, 375-379. - Brown, L.D., Cai, T. T., & DasGupta, A. (2003).
Interval estimation in exponential families.
Statistica Sinica 13, 19-49. - Brown, L.D., Cai, T. T., & DasGupta, A. (2002).
Confidence intervals for a binomial proportion and asymptotic expansions.
The Annals of Statistics 30, 160-201. - Brown, L.D., Cai, T. T., & DasGupta, A. (2001).
Interval estimation for a binomial proportion (with discussion).
Statistical Science 16, 101-133. - Liao, K. P., Sparks, J. A., Hejblum, B., Kuo, I-H., Cui, J., Lahey, L., Cagan, A., Gainer, V., Liu, W., Cai, T. T., Sokolove, J., & Cai, T. (2017).
Phenome-wide association study of autoantibodies to citrullinated and non-citrullinated epitopes in rheumatoid arthritis.
Arthritis & Rheumatology 69, 742-749. - Jeng, J., Cai, T. T., & Li, H. (2013).
Simultaneous discovery of rare and common segment variants.
Biometrika 100, 157-172. - Cai, T. T., Li, H., Liu, W., & Xie, J. (2013).
Covariate adjusted precision matrix estimation with an application in genetical genomics.
Biometrika 100, 139-156. - Cai, T. T., Jeng, J., & Li, H. (2012).
Robust detection and identification of sparse segments in ultra-high dimensional data analysis.
Journal of the Royal Statistical Society, Series B 74, 773-797. - Xie, J., Cai, T. T., & Li, H. (2010).
Sample size and power analysis for sparse signal recovery in genome-wide association studies.
Biometrika 98, 273-290. - Jeng, J., Cai, T. T., & Li, H. (2010).
Optimal sparse segment identification with application in copy number variation analysis.
Journal of the American Statistical Association 105, 1156-1166. - Jin, J. & Cai, T. T. (2007).
Estimating the null and the proportion of non-null effects in large-scale multiple comparisons.
Journal of the American Statistical Association 102, 495-506. - Sun, W. & Cai, T. T. (2007).
Oracle and adaptive compound decision rules for false discovery rate control.
Journal of the American Statistical Association 102, 901-912. - Cai, T. T., Zhang, D., & Ben-Amotz, D. (2001).
Enhanced chemical classification of Raman images using wavelet transformation.
Applied Spectroscopy 55, 1124-1130. - Shyu, C-R., Cai, T. T., & Broderick, L.S. (1999).
On archiving and retrieval of sequential images from tomographic databases in PACS.
Proc. SPIE - the International Society for Optical Engineering 3656, 33-40.