Sloan Nietert, Ziv Goldfeld, and Kengo Kato. From Smooth Wasserstein Distance to Dual Sobolev Norm: Empirical Approximation and Statistical Applications, 2021b.

Jonathan Niles-Weed and Quentin Berthet. Minimax estimation of smooth densities in Wasserstein distance. *The Annals of Statistics*, 50, 2022.

Gabriel Peyré and Marco Cuturi. Computational Optimal Transport. *Foundations and Trends in Machine Learning*, 11, 2019.

Jr. R. P. Boas and M. Kac. Inequalities for Fourier transforms of positive functions. *Duke Mathematical Journal*, 12, 1945.

Ali Rahimi and Benjamin Recht. Random Features for Large-Scale Kernel Machines. In *Advances in Neural Information Processing Systems (NeurIPS)*, 2007.

Ali Rahimi and Benjamin Recht. Weighted Sums of Random Kitchen Sinks: Replacing Minimization with Randomization in Learning. In *Advances in Neural Information Processing Systems (NeurIPS)*, 2008.

Carl Edward Rasmussen and Christopher K. I. Williams. *Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)*. The MIT Press, 2005.

Mark D. Reid and Robert C. Williamson. Information, Divergence and Risk for Binary Experiments. *Journal of Machine Learning Research (JMLR)*, 12, 2011.

Philippe Rigollet and Jonathan Weed. Entropic optimal transport is maximum-likelihood deconvolution. *Comptes Rendus Mathematique*, 356, 2018.

E.B. Saff and V. Totik. *Logarithmic Potentials with External Fields*. Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 2013.

Filippo Santambrogio. *Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling*. Progress in Nonlinear Differential Equations and Their Applications. Springer International Publishing, 2015.

Vincent Schellekens and Laurent Jacques. Compressive Classification (Machine Learning without learning), 2018.

Vincent Schellekens and Laurent Jacques. Compressive Learning of Generative Networks, 2020.

Dino Sejdinovic, Bharath Sriperumbudur, Arthur Gretton, and Kenji Fukumizu. Equivalence of distance-based and RKHS-based statistics in hypothesis testing. *The Annals of Statistics*, 41, 2013.

Shai Shalev-Shwartz and Shai Ben-David. *Understanding Machine Learning: From Theory to Algorithms*. Cambridge University Press, 2014.

Hui Shi, Yann Traonmilin, and Jean-François Aujol. Compressive learning of deep regularization for denoising. *2022a*.

Hui Shi, Yann Traonmilin, and Jean-François Aujol. Compressive learning for patch-based image denoising. *SIAM Journal on Imaging Sciences*, 15(3), 2022b.

Carl-Johann Simon-Gabriel, Alessandro Barp, and Lester Mackey. Metrizing Weak Convergence with Maximum Mean Discrepancies, 2020.

Justin Solomon, Raif Rustamov, Leonidas Guibas, and Adrian Butscher. Wasserstein Propagation for Semi-Supervised Learning. In *International Conference on Machine Learning (ICML)*, 2014.
Bharath Sriperumbudur and Zoltan Szabo. Optimal Rates for Random Fourier Features. In *Advances in Neural Information Processing Systems (NeurIPS)*, 2015.

Bharath K. Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Bernhard Schölkopf, and Gert R. G. Lanckriet. On integral probability metrics, phi-divergences and binary classification, 2009.

Bharath K. Sriperumbudur, Arthur Gretton, Kenji Fukumizu, Bernhard Schölkopf, and Gert R.G. Lanckriet. Hilbert Space Embeddings and Metrics on Probability Measures. *Journal of Machine Learning Research* (JMLR), 11, 2010.

Bharath K. Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Bernhard Schölkopf, and Gert R. G. Lanckriet. On the empirical estimation of integral probability metrics. *Electronic Journal of Statistics*, 6, 2012.

Elias M. Stein and Guido Weiss. *Introduction to Fourier Analysis on Euclidean Spaces*. Princeton University Press, 2016.

Ingo Steinwart and Andreas Christmann. *Support vector machines*. Springer Science & Business Media, 2008.

Danica J. Sutherland and Jeff Schneider. On the Error of Random Fourier Features, 2015.

Gabor Szekely and Maria Rizzo. Testing for equal distributions in high dimension. *InterStat*, 5, 2004.

Gábor J. Székely and Maria L. Rizzo. The Energy of Data. *Annual Review of Statistics and Its Application*, 4, 2017.

Madeleine Udell, Corinne Horn, Reza Zadeh, and Stephen Boyd. Generalized Low Rank Models. *Foundations and Trends in Machine Learning*, 9, 2016.

Cédric Villani. *Optimal Transport: Old and New*. Springer, 2008.

Aladin Virmaux and Kevin Scaman. Lipschitz regularity of deep neural networks: analysis and efficient estimation. In *Advances in Neural Information Processing Systems (NeurIPS)*, 2018.

Jonathan Weed and Francis Bach. Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. *Bernoulli*, 25, 2019.

Holger Wendland. Scattered Data Approximation. *Cambridge University Press*, 2004.

Yixing Zhang, Xiuyuan Cheng, and Galen Reeves. Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples. In *International Conference on Artificial Intelligence and Statistics (AISTATS)*, 2021.