[41] J. Kwon, N. Ho, and C. Caramanis. On the minimax optimality of the EM algorithm for learning two-component mixed linear regression. In AISTATS, 2021.
[42] J. Kwon, W. Qian, C. Caramanis, Y. Chen, and D. Davis. Global Convergence of the EM Algorithm for Mixtures of Two Component Linear Regression. In A. Beygelzimer and D. Hsu, editors, Proceedings of the Thirty-Second Conference on Learning Theory, volume 99 of Proceedings of Machine Learning Research, pages 2055–2110. PMLR, June 2019.
[43] Q. Li, R. Shi, , and F. Liang. Drug sensitivity prediction with high-dimensional mixture regression. PLoS ONE, 2019.
[44] H. Liang, Z. Fan, R. Sarkar, Z. Jiang, T. Chen, K. Zou, Y. Cheng, C. Hao, and Z. Wang.  $\mathbf{M}^3\mathrm{ViT}$ : Mixture-of-Experts Vision Transformer for Efficient Multi-task Learning with Model-Accelerator Co-design. In NeurIPS, 2022.
[45] J. Ma, Z. Zhao, X. Yi, J. Chen, L. Hong, and E. H. Chi. Modeling Task Relationships in Multi-Task Learning with Multi-Gate Mixture-of-Experts. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, KDD '18, pages 1930–1939, New York, NY, USA, 2018. Association for Computing Machinery. event-place: London, United Kingdom.
[46] T. Manole and N. Ho. Uniform convergence rates for maximum likelihood estimation under two-component gaussian mixture models. arXiv preprint arXiv:2006.00704, 2020.
[47] T. Manole and N. Ho. Refined convergence rates for maximum likelihood estimation under finite mixture models. In Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pages 14979-15006. PMLR, 17-23 Jul 2022.
[48] L. Montuelle and E. Le Pennec. Mixture of Gaussian regressions model with logistic weights, a penalized maximum likelihood approach. *Electronic Journal of Statistics*, 8(1):1661–1695, 2014.
[49] B. Mustafa, C. Ruiz, J. Puigcerver, R. Jenatton, and N. Houlsby. Multimodal contrastive learning with limoe: the language-image mixture of experts. In NeurIPS, 2022.
[50] X. Nguyen. Convergence of latent mixing measures in finite and infinite mixture models. Annals of Statistics, 4(1):370-400, 2013.
[51] F. Peng, R. A. Jacobs, and M. A. Tanner. Bayesian Inference in Mixtures-of-Experts and Hierarchical Mixtures-of-Experts Models With an Application to Speech Recognition. Journal of the American Statistical Association, 91(435):953–960, 1996.
[52] C. Ruiz, J. Puigcerver, B. Mustafa, M. Neumann, R. Jenatton, A. Pinto, D. Keysers, and N. Houlsby. Scaling vision with sparse mixture of experts. In NeurIPS, 2021.
[53] M. E. Ruiz and P. Srinivasan. Hierarchical Text Categorization Using Neural Networks. Information Retrieval, 5(1):87-118, Jan. 2002.
[54] N. Shazeer, A. Mirhoseini, K. Maziarz, A. Davis, Q. Le, G. Hinton, and J. Dean. Outrageously large neural networks: The sparsely-gated mixture-of-experts layer. In International Conference on Learning Representations (ICLR), 2017.
[55] B. Sturmfels. Solving Systems of Polynomial Equations. Providence, R.I, 2002.
[56] H. Teicher. On the mixture of distributions. Annals of Statistics, 31:55-73, 1960.
[57] H. Teicher. Identifiability of mixtures. Annals of Statistics, 32:244-248, 1961.
[58] S. van de Geer. Empirical processes in  $M$ -estimation. Cambridge University Press, 2000.
[59] C. Villani. Optimal transport: Old and New. Springer, 2008.
[60] S. Waterhouse and A. Robinson. Classification using hierarchical mixtures of experts. In Proceedings of IEEE Workshop on Neural Networks for Signal Processing, pages 177-186, 1994.
[61] Y. Wu and P. Yang. Optimal estimation of Gaussian mixtures via denoised method of moments. The Annals of Statistics, 48:1987-2007, 2020.
[62] Y. Wu and H. H. Zhou. Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in  $o(\sqrt{n})$  iterations. Mathematical Statistics and Learning, 4:143-220, 2021.