Raymond J Carroll and Peter Hall. Optimal rates of convergence for deconvolving a density. Journal of the American Statistical Association, 83(404):1184-1186, 1988.
Bruce G Lindsay and Kathryn Roeder. Uniqueness of estimation and identifiability in mixture models. Canadian Journal of Statistics, 21(2):139-147, 1993.
Imre Csiszár. On the computation of rate-distortion functions (corresp.). IEEE Transactions on Information Theory, 20(1):122-124, 1974b. doi: 10.1109/TIT.1974.1055146.
Imre Csiszár. Information geometry and alternating minimization procedures. Statistics and Decisions, Dedewicz, 1:205-237, 1984.
Robert M. Gray and David L. Neuhoff. Quantization. IEEE transactions on information theory, 44 (6):2325-2383, 1998.
George Papamakarios, Eric Nalisnick, Danilo Jimenez Rezende, Shakir Mohamed, and Balaji Lakshminarayanan. Normalizing flows for probabilistic modeling and inference. The Journal of Machine Learning Research, 22(1):2617-2680, 2021.
Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114, 2013.
Shitong Wu, Wenhao Ye, Hao Wu, Huihui Wu, Wenyi Zhang, and Bo Bai. A communication optimal transport approach to the computation of rate distortion functions. arXiv preprint arXiv:2212.10098, 2022.
Eric Lei, Hamed Hassani, and Shirin Saeedi Bidokhti. On a relation between the rate-distortion function and optimal transport, 2023b.
Aude Geneva, Lénaic Chizat, Francis Bach, Marco Cuturi, and Gabriel Peyré. Sample complexity of Sinkhorn divergences. In The 22nd International Conference on Artificial Intelligence and Statistics, pages 1574-1583. PMLR, 2019.
Philippe Rigollet and Austin J Stromme. On the sample complexity of entropic optimal transport. arXiv preprint arXiv:2206.13472, 2022.
Yuling Yan, Kaizheng Wang, and Philippe Rigollet. Learning gaussian mixtures using the wasserstein-fisher-rao gradient flow. arXiv preprint arXiv:2301.01766, 2023.
Lenaic Chizat, Gabriel Peyre, Bernhard Schmitzer, and François-Xavier Vialard. An interpolating distance between optimal transport and fisher-rao metrics. Foundations of Computational Mathematics, 18:1-44, 2018.
Lenaic Chizat. Mean-field Langevin dynamics: Exponential convergence and annealing. arXiv preprint arXiv:2202.01009, 2022.
Marcel Nutz. Introduction to entropic optimal transport. Lecture notes, Columbia University, 2021. https://www.math.columbia.edu/~mnutz/docs/EOT_lecture_notes.pdf.
Guillaume Carlier, Lénaïc Chizat, and Maxime Laborde. Lipschitz continuity of the Schrödinger map in entropic optimal transport. arXiv preprint arXiv:2210.00225, 2022.
Toby Berger. Rate distortion theory, a mathematical basis for data compression. Prentice Hall, 1971.
Stephan Eckstein and Marcel Nutz. Convergence rates for regularized optimal transport via quantization. arXiv preprint arXiv:2208.14391, 2022.
Eric Lei, Hamed Hassani, and Shirin Saeedi Bidokhti. Neural estimation of the rate-distortion function for massive datasets. In 2022 IEEE International Symposium on Information Theory (ISIT), pages 608-613. IEEE, 2022.
Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278-2324, 1998.