[37] Sreejith Sreekumar, Zhengxin Zhang, and Ziv Goldfeld. Non-asymptotic performance guarantees for neural estimation of f-divergences. In International Conference on Artificial Intelligence and Statistics, pages 3322-3330. PMLR, 2021.
[38] Sreejith Sreekumar and Ziv Goldfeld. Neural estimation of statistical divergences. Journal of Machine Learning Research, 23(126):1-75, 2022.
[39] Yanzhi Chen, Weihao Sun, Yingzhen Li, and Adrian Weller. Scalable infomin learning. Advances in Neural Information Processing Systems, 35:2226-2239, 2022.
[40] Thomas M Cover and A Joy Thomas. Elements of Information Theory. Wiley, New-York, 2nd edition, 2006.
[41] Julien Rabin, Gabriel Peyré, Julie Delon, and Marc Bernot. Wasserstein barycenter and its application to texture mixing. In Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29-June 2, 2011, Revised Selected Papers 3, pages 435-446. Springer, 2012.
[42] Ishan Deshpande, Yuan-Ting Hu, Ruoyu Sun, Ayis Pyrros, Nasir Siddiqui, Sanmi Koyejo, Zhizhen Zhao, David Forsyth, and Alexander G Schwing. Max-sliced wasserstein distance and its use for gans. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10648-10656, 2019.
[43] Soheil Kolouri, Kimia Nadjahi, Umut Simsekli, Roland Badeau, and Gustavo Rohde. Generalized sliced Wasserstein distances. Advances in neural information processing systems, 32, 2019.
[44] Tianyi Lin, Chenyou Fan, Nhat Ho, Marco Cuturi, and Michael Jordan. Projection robust Wasserstein distance and riemannian optimization. Advances in neural information processing systems, 33:9383-9397, 2020.
[45] Minhui Huang, Shiqian Ma, and Lifeng Lai. A riemannian block coordinate descent method for computing the projection robust Wasserstein distance. In International Conference on Machine Learning, pages 4446-4455. PMLR, 2021.
[46] Tianyi Lin, Zeyu Zheng, Elynn Chen, Marco Cuturi, and Michael I Jordan. On projection robust optimal transport: Sample complexity and model misspecification. In International Conference on Artificial Intelligence and Statistics, pages 262-270. PMLR, 2021.
[47] Sloan Nietert, Ziv Goldfeld, Ritwik Sadhu, and Kengo Kato. Statistical, robustness, and computational guarantees for sliced wasserstein distances. Advances in Neural Information Processing Systems, 35:28179-28193, 2022.
[48] C Radhakrishna Rao. Separation theorems for singular values of matrices and their applications in multivariate analysis. Journal of Multivariate Analysis, 9(3):362-377, 1979.
[49] Karl Pearson. Liii. on lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin philosophical magazine and journal of science, 2(11):559-572, 1901.
[50] Wojciech Marian Czarnecki, Rafal Jozefowicz, and Jacek Tabor. Maximum entropy linear manifold for learning discriminative low-dimensional representation. In Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2015, Porto, Portugal, September 7-11, 2015, Proceedings, Part I 15, pages 52-67. Springer, 2015.
[51] Michael Tschannen, Josip Djolonga, Paul K Rubenstein, Sylvain Gelly, and Mario Lucic. On mutual information maximization for representation learning. Proceedings of the International Conference on Learning Representations (ICLR), 2020.
[52] Jason M Klusowski and Andrew R Barron. Approximation by combinations of relu and squared relu ridge functions with  $\ell^1$  and  $\ell^0$  controls. IEEE Transactions on Information Theory, 64(12):7649-7656, 2018.
[53] Andrew R Barron. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information theory, 39(3):930-945, 1993.