[16] Diakonikolas, I., Gouleakis, T., Kane, D. M., Peebles, J., and Price, E. Optimal testing of discrete distributions with high probability. In Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pages 542-555, 2021.
[17] Diggle, P. J. and Gratton, R. J. Monte carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society: Series B (Methodological), 46(2):193-212, 1984.
[18] Gerber, P. R. and Polyanskiy, Y. Likelihood-free hypothesis testing. CoRR, abs/2211.01126, 2022. doi: 10.48550/arXiv.2211.01126.
[19] Gerber, P. R., Han, Y., and Polyanskiy, Y. Minimax optimal testing by classification, 2023.
[20] Gretton, A., Fukumizu, K., Harchaoui, Z., and Sriperumbudur, B. K. A fast, consistent kernel two-sample test. Advances in neural information processing systems, 22, 2009.
[21] Gretton, A., Borgwardt, K. M., Rasch, M. J., Scholkopf, B., and Smola, A. A kernel two-sample test. The Journal of Machine Learning Research, 13(1):723-773, 2012.
[22] Gretton, A., Sejdinovic, D., Strathmann, H., Balakrishnan, S., Pontil, M., Fukumizu, K., and Sriperumbudur, B. K. Optimal kernel choice for large-scale two-sample tests. Advances in neural information processing systems, 25, 2012.
[23] Gutman, M. Asymptotically optimal classification for multiple tests with empirically observed statistics. IEEE Transactions on Information Theory, 35(2):401-408, 1989.
[24] Gutmann, M. U., Dutta, R., Kaski, S., and Corander, J. Likelihood-free inference via classification. Statistics and Computing, 28:411-425, 2018.
[25] Ho, J., Jain, A., and Abbeel, P. Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems, 33:6840-6851, 2020.
[26] Huang, D. Hypothesis Testing and Learning with Small Samples. PhD thesis, CiteSeer, 2012.
[27] Huang, D. and Meyn, S. Classification with high-dimensional sparse samples. In 2012 IEEE International Symposium on Information Theory Proceedings, pages 2586-2590. IEEE, 2012.
[28] Ingster, Y. I. Minimax testing of nonparametric hypotheses on a distribution density in the  $l_p$  metrics. Theory of Probability & Its Applications, 31(2):333-337, 1987. doi: 10.1137/1131042.
[29] Izbicki, R., Lee, A., and Schafer, C. High-dimensional density ratio estimation with extensions to approximate likelihood computation. In Artificial intelligence and statistics, pages 420-429. PMLR, 2014.
[30] Jiang, B., Wu, T.-y., Zheng, C., and Wong, W. H. Learning summary statistic for approximate bayesian computation via deep neural network. Statistica Sinica, pages 1595-1618, 2017.
[31] Jitkrittum, W., Kanagawa, H., Sangkloy, P., Hays, J., Scholkopf, B., and Gretton, A. Informative features for model comparison. Advances in Neural Information Processing Systems, 31, 2018.
[32] Kelly, B. G., Tularak, T., Wagner, A. B., and Viswanath, P. Universal hypothesis testing in the learning-limited regime. In 2010 IEEE International Symposium on Information Theory, pages 1478-1482. IEEE, 2010.
[33] Kelly, B. G., Wagner, A. B., Tularak, T., and Viswanath, P. Classification of homogeneous data with large alphabets. IEEE transactions on information theory, 59(2):782-795, 2012.
[34] Kingma, D. P. and Ba, J. Adam: A method for stochastic optimization. In Bengio, Y. and LeCun, Y., editors, 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings, 2015.
[35] Krizhevsky, A. Learning multiple layers of features from tiny images. University of Toronto, 2009.
[36] Krizhevsky, A., Nair, V., and Hinton, G. The cifar-10 dataset (2014). Online: http://www.cs.toronto.edu/kriz/cifar.html, 55, 2020.
[37] Li, T. and Yuan, M. On the optimality of gaussian kernel based nonparametric tests against smooth alternatives. arXiv preprint arXiv:1909.03302, 2019.
[38] List, L. Statistical methods for data analysis in particle physics, volume 941. Springer, 2017.
[39] Liu, F., Xu, W., Lu, J., Zhang, G., Gretton, A., and Sutherland, D. J. Learning deep kernels for non-parametric two-sample tests. In International conference on machine learning, pages 6316-6326. PMLR, 2020.