Arora, S., Ge, R., Liang, Y., Ma, T., and Zhang, Y. (2017). Generalization and equilibrium in generative adversarial nets (GANs). In International Conference on Machine Learning, pages 224-232. PMLR.
Barrett, B., Camuto, A., Willetts, M., and Rainforth, T. (2022). Certifiably robust variational autoencoders. In International Conference on Artificial Intelligence and Statistics, pages 3663-3683. PMLR.
Biau, G., Sangnier, M., and Tanielian, U. (2021). Some theoretical insights into Wasserstein GANs. Journal of Machine Learning Research.
Björck, Å. and Bowie, C. (1971). An iterative algorithm for computing the best estimate of an orthogonal matrix. SIAM Journal on Numerical Analysis, 8(2):358-364.
Boucheron, S., Lugosi, G., and Massart, P. (2013). Concentration inequalities: A nonasymptotic theory of independence. Oxford university press.
Bowman, S. R., Vilnis, L., Vinyals, O., Dai, A. M., Józefowicz, R., and Bengio, S. (2016). Generating sentences from a continuous space. In Conference on Computational Natural Language Learning, CoNLL, pages 10-21. ACL.
Catoni, O. (2003). A PAC-Bayesian approach to adaptive classification. preprint LPMA, 840.
Chakrabarty, A. and Das, S. (2021). Statistical regeneration guarantees of the Wasserstein autoencoder with latent space consistency. In Advances in Neural Information Processing Systems.
Chérief-Abdellatif, B.-E., Shi, Y., Doucet, A., and Guedj, B. (2022). On PAC-Bayesian reconstruction guarantees for VAEs. In International Conference on Artificial Intelligence and Statistics, pages 3066-3079. PMLR.
Chu, J. T. (1955). On bounds for the normal integral. Biometrika, 42(1/2):263-265.
Donsker, M. D. and Varadhan, S. S. (1976). Asymptotic evaluation of certain markov process expectations for large time—iii. Communications on pure and applied Mathematics, 29(4):389-461.
Dziugaite, G. K. and Roy, D. M. (2018). Data-dependent PAC-Bayes priors via differential privacy. In Advances in Neural Information Processing Systems, volume 31.
Fazlyab, M., Robey, A., Hassani, H., Morari, M., and Pappas, G. (2019). Efficient and accurate estimation of Lipschitz constants for deep neural networks. In Advances in Neural Information Processing Systems, volume 32.
Fefferman, C., Mitter, S., and Narayanan, H. (2016). Testing the manifold hypothesis. Journal of the American Mathematical Society, 29(4):983-1049.
Fodor, I. K. (2002). A survey of dimension reduction techniques. Technical report, Lawrence Livermore National Lab., CA (US).
Germain, P., Bach, F., Lacoste, A., and Lacoste-Julien, S. (2016). PAC-Bayesian theory meets Bayesian inference. In Advances in Neural Information Processing Systems, volume 29.
Germain, P., Habrard, A., Laviolette, F., and Morvant, E. (2020). PAC-Bayes and domain adaptation. Neurocomputing, 379:379-397.
Germain, P., Lacasse, A., Laviolette, F., and Marchand, M. (2009). PAC-Bayesian learning of linear classifiers. In International Conference on Machine Learning, page 353-360.
Givens, C. R. and Shortt, R. M. (1984). A class of Wasserstein metrics for probability distributions. Michigan Mathematical Journal, 31(2):231-240.
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. (2014). Generative adversarial nets. In Advances in Neural Information Processing Systems, volume 27.