Stanislav Minsker - Publications

Papers

• Improved performance guarantees for Tukey's median (with Yinan Shen, 2024).
  https://arxiv.org/abs/2410.00219

• Concentration and moment inequalities for heavy-tailed random matrices (with M. Jirak, M. Wahl and Yiqiu Shen, 2024).
  https://arxiv.org/abs/2407.12948

• The geometric median and applications to robust mean estimation (with N. Strawn, 2024). SIAM Journal on Mathematics of Data Science, Vol. 6(2), p. 504-533.
  https://arxiv.org/abs/2307.03111

• Efficient median of means estimator. In COLT 2023, 36th Conference on Learning Theory.
  https://arxiv.org/abs/2305.18681

• Robust and tuning-free sparse linear regression via square-root Slope (with M. Ndaoud and L. Wang, 2024). SIAM Journal on Mathematics of Data Science, Vol. 6(2), p. 428-453.
  https://arxiv.org/abs/2210.16808

• Median of means principle for Bayesian inference (with S. Yao, 2022).
  https://arxiv.org/abs/2203.06617

• U-statistics of growing order and sub-Gaussian mean estimators with sharp constants (2023). Mathematical Statistics and Learning, Vol. 7(1), p. 1-39.
  https://arxiv.org/abs/2202.11842

• Minimax Supervised Clustering in the Anisotropic Gaussian Mixture Model: A new take on Robust Interpolation (with M. Ndaoud and Y. Shen, 2021).
  https://arxiv.org/abs/2111.07041

• Robust estimation of covariance matrices: adversarial contamination and beyond (with L. Wang, 2024). Statistica Sinica, Vol. 34, p. 1565-1583.
  https://arxiv.org/abs/2203.02880

• Robust and efficient mean estimation: approach based on the properties of self-normalized sums (with M. Ndaoud, 2021). Electronic Journal of Statistics, Vol. 15(2), p. 6036-6070.
  arXiv:2006.01986

• Asymptotic normality of robust risk minimizers. Submitted (2020).
  arXiv:2004.02328.

• Robust modifications of U-statistics and applications to covariance estimation problems (with X. Wei, 2020). Bernoulli 26, No. 1, 694-727.
  arXiv:1801.05565

• Excess risk bounds in robust empirical risk minimization (with T. Matthieu). Information and Inference: A Journal of the IMA, Vol. 10(4), 1423-1490 (2021).
  arXiv:1910.07485

• Uniform bounds for robust mean estimators. Submitted (2019).
  arXiv:1812.03523

• User-friendly covariance estimation for heavy-tailed distributions: a survey and recent results (with Yuan Ke, Zhao Ren, Qiang Sun and Wen-Xin Zhou, 2019). Statistical Science, vol. 34, No. 3, 454-471.
  arXiv:1811.01520

• Moment inequalities for matrix-valued U-statistics of order 2 (with X. Wei, 2019). Electronic Journal of Probability 24, No. 133, 1-32.
  arXiv:1801.05921

• Distributed statistical estimation and rates of convergence in normal approximation (2019). Electronic Journal of Statistics, Vol. 13(2), 5213-5252.
  PDF of the most recent version; also see arXiv:1704.02658 for an older version of the paper.

• Structured signal recovery from non-linear and heavy-tailed measurements (with L. Goldstein and X. Wei, 2018). IEEE Transactions on Information Theory,Vol. 64, Iss. 8, pages 5513 - 5530.
  arXiv:1609.01025.

• Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries (2018). Annals of Statistics, Vol. 46, pages 2871-2903.
  arXiv:1605.07129.

• Estimation of the covariance structure of heavy-tailed distributions (with X. Wei, 2017). Neural Information Processing Systems (NeurIPS).
  arXiv:1708.00502.

• Multiscale Dictionary Learning: Non-Asymptotic Bounds and Robustness (with M. Maggioni and N. Strawn, 2016). Journal of Machine Learning Research, 17(2):1-51.
  Abstract and PDF.
  Code on M. Maggioni's webpage.

• Geometric Median and Robust Estimation in Banach Spaces (2015). Bernoulli 21, no. 4, 2308-2335.
  arXiv:1308.1334

• On some extensions of Bernstein's inequality for self-adjoint operators (2017). Statistics and Probability Letters, 127, p. 111-119.
  arXiv:1112.5448

• Functional linear model with subgaussian design: - penalization approach (with V. Koltchinskii, 2014). Journal de l’Ecole Polytechnique – Mathematiques, 1, p. 269-330.
  PDF.

• Robust and scalable Bayes via a median of subset posterior measures (with S. Srivastava, L. Lin and D. Dunson, 2017). Journal of Machine Learning Research, 18(124):1−40.
  arXiv:1403.2660
  M-posterior code is available here; R package can be downloaded here.

• Active Learning for Personalized Medicine (with G. Cheng and Y. Zhao, 2015). Journal of the American Statistical Association, vol. 111, number 514, p. 875-887.
  arXiv:1404.2971

• Scalable and Robust Bayesian Inference via the Median Posterior (with S. Srivastava, L. Lin and D. Dunson). In ICML 2014, 31st International Conference on Machine Learning.
  PDF.

• Multiscale Dictionary and Manifold Learning: Non-Asymptotic Bounds for the Geometric Multi-Resolution Analysis (with M. Maggioni and N. Strawn). In iTWIST 2014, International Traveling Workshop on Interactions between Space Models and Technology.
  Conference Proceedings.

• Learning Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling. In COLT 2013, 26th Conference on Learning Theory.
  Abstract and PDF.

• Plug-in approach to Active Learning (2012). Journal of Machine Learning Research 13, p. 67-90.
  Abstract and PDF.
  Improved version of some bounds can be found in Chapter 2 of my Ph.D. thesis.

• Sparse recovery in convex hulls of infinite dictionaries (with V. Koltchinskii). In COLT 2010, 23rd Conference on Learning Theory.
  PDF.
  Extended version is included in Chapter 3 of my Ph.D. thesis.

Ph.D. Thesis

Non-Asymptotic Bounds for Prediction Problems and Density Estimation. Georgia Institute of Technology, 2012. PDF.