Avishek Ghosh, Ashwin Pananjady, Adityanand Guntuboyina, and Kannan Ramchandran. Max-affine regression: Parameter estimation for gaussian designs. IEEE Transactions on Information Theory, 2021.
Adityanand Guntuboyina. Optimal rates of convergence for convex set estimation from support functions. The Annals of Statistics, 40(1):385-411, 2012.
Qiyang Han and Jon A Wellner. Multivariate convex regression: global risk bounds and adaptation. arXiv preprint arXiv:1601.06844, 2016.
Qiyang Han, Tengyao Wang, Sabyasachi Chatterjee, and Richard J Samworth. Isotonic regression in general dimensions. The Annals of Statistics, 47(5):2440-2471, 2019.
Trevor Hastie, Andrea Montanari, Saharon Rosset, and Ryan J Tibshirani. Surprises in high-dimensional ridgeless least squares interpolation. The Annals of Statistics, 50(2):949-986, 2022.
Adel Javanmard and Andrea Montanari. Debiasing the lasso: Optimal sample size for gaussian designs. The Annals of Statistics, 46(6A):2593-2622, 2018.
Arlene KH Kim and Richard J Samworth. Global rates of convergence in log-concave density estimation. The Annals of Statistics, 44(6):2756-2779, 2016.
Vladimir Koltchinskii. Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems: Ecole d'Eté de Probabilités de Saint-Flour XXXVIII-2008, volume 2033. Springer Science & Business Media, 2011.
Gil Kur and Alexander Rakhlin. On the minimal error of empirical risk minimization. In Conference on Learning Theory, pages 2849-2852. PMLR, 2021.
Gil Kur, Yuval Dagan, and Alexander Rakhlin. Optimality of maximum likelihood for log-concave density estimation and bounded convex regression. arXiv preprint arXiv:1903.05315, 2019.
Gil Kur, Fuchang Gao, Adityanand Guntuboyina, and Bodhisattva Sen. Convex regression in multidimensions: Suboptimality of least squares estimators. arXiv preprint arXiv:2006.02044, 2020a.
Gil Kur, Alexander Rakhlin, and Adriyanand Guntuboyina. On suboptimality of least squares with application to estimation of convex bodies. In Conference on Learning Theory, pages 2406-2424. PMLR, 2020b.
Guillaume Lecué and Shahar Mendelson. Learning subgaussian classes: Upper and minimax bounds. arXiv preprint arXiv:1305.4825, 2013.
Michel Ledoux. The concentration of measure phenomenon. Number 89 in Mathematical Surveys and Monographs. American Mathematical Soc., 2001.
Wee Sun Lee, Peter L Bartlett, and Robert C Williamson. The importance of convexity in learning with squared loss. In Proceedings of the Ninth Annual Conference on Computational Learning Theory, pages 140-146, 1996.
Tengyuan Liang and Alexander Rakhlin. Just interpolate: Kernel "ridgeless" regression can generalize. The Annals of Statistics, 48(3):1329-1347, 2020.
Tengyuan Liang, Alexander Rakhlin, and Xiyu Zhai. On the multiple descent of minimum-norm interpolants and restricted lower isometry of kernels. In Conference on Learning Theory, pages 2683-2711. PMLR, 2020.
Shahar Mendelson. Learning without concentration. In Conference on Learning Theory, pages 25-39, 2014.
Shahar Mendelson. Extending the scope of the small-ball method. arXiv preprint arXiv:1709.00843, 2017.
Emanuel Milman. On the role of convexity in isoperimetry, spectral gap and concentration. Inventiones mathematicae, 177(1):1-43, 2009.