[34] A. Cohen and G. Migliorati. Optimal weighted least-squares methods. *SMAI J. Comput. Math.*, 3:181-203, 2017.
[35] E. C. Cyr, M. A. Gulian, R. G. Patel, M. Perego, and N. A. Trask. Robust training and initialization of deep neural networks: An adaptive basis viewpoint. In Jianfeng Lu and Rachel Ward, editors, Proceedings of The First Mathematical and Scientific Machine Learning Conference, volume 107 of Proceedings of Machine Learning Research, pages 512-536, Princeton University, Princeton, NJ, USA, 2020. PMLR.
[36] W. M. Czarnecki, S. Osindero, M. Jaderberg, G. Swirszcz, and R. Pascanu. Sobolev training for neural networks. In I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017.
[37] D. Düng, V. Temlyakov, and T. Ullrich. Hyperbolic Cross Approximation. Adv. Courses Math. CRM Barcelona. Birkhäuser, Basel, Switzerland, 2018.
[38] M. A. Davenport and J. Romberg. An overview of low-rank matrix recovery from incomplete observations. IEEE J. Sel. Topics Signal Process., 10(4):602-622, 2016.
[39] T. De Ryck and S. Mishra. Generic bounds on the approximation error for physics-informed (and) operator learning. In Alice H. Oh, Alekh Agarwal, Danielle Belgrave, and Kyunghyun Cho, editors, Advances in Neural Information Processing Systems, 2022.
[40] P. Deora, B. Vasudeva, S. Bhattacharya, and P. M. Pradhan. Structure preserving compressive sensing MRI reconstruction using generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 522-523, 2020.
[41] M. Derezinski, M. K. K Warmuth, and D. J. Hsu. Leveraged volume sampling for linear regression. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018.
[42] W. E, J. Han, and A. Jentzen. Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Commun. Math. Stat., 5(4):349-380, 2017.
[43] M. Eigel, R. Schneider, and P. Trunschke. Convergence bounds for empirical nonlinear least-squares. ESAIM Math. Model. Numer. Anal., 56(1):79-104, 2022.
[44] M. S. Eldred, L. W. T. Ng, M. F. Barrone, and S. P. Domino. Multifidelity uncertainty quantification using spectral stochastic discrepancy models. In Roger Ghanem, David Higdon, and Houman Owhadi, editors, Handbook of Uncertainty Quantification, pages 991-1036. Springer, Cham, Switzerland, 2017.
[45] C. L. Epstein. Introduction to the Mathematics of Medical Imaging. Other Titles in Applied Mathematics. Society for Industrial and Applied Mathematics, 2nd edition, 2007.
[46] T. Erdelyi, C. Musco, and C. Musco. Fourier sparse leverage scores and approximate kernel learning. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 109-122. Curran Associates, Inc., 2020.
[47] M. Fanuel, J. Schreurs, and J. A. K. Suykens. Nyström landmark sampling and regularized Christoffel functions. Mach. Learn., 111:2213-2254, 2022.
[48] S. Foucart and H. Rauhut. A Mathematical Introduction to Compressive Sensing. Appl. Numer. Harmon. Anal. Birkhäuser, New York, NY, 2013.
[49] A. Gajjar, C. Hegde, and C. P. Musco. Provable active learning of neural networks for parametric PDEs. In The Symbiosis of Deep Learning and Differential Equations II, 2022.