Textbooks: We recommend the following books, although we will not follow them closely.
High-dimensional statistics: A non-asymptotic viewpoint, Martin J. Wainwright, 2019.
Statistical foundations of data science, Jianqing Fan, Runze Li, Cun-Hui Zhang, Hui Zou, Chapman and Hall, 2020.
High-dimensional probability: An introduction with applications in data science, Roman Vershynin, Cambridge University Press, 2018.
References: The following references also contain topics relevant to this course, and you might want to consult them.
Spectral methods for data science: A statistical perspective, Yuxin chen, Yuejie Chi, Jianqing Fan, Cong Ma, to appear in Foundations and Trends® in Machine Learning, 2021.
Nonconvex optimization meets low-rank matrix factorization: An overview, Yuejie Chi, Yue M. Lu, Yuxin Chen, IEEE Transactions on Signal Processing, vol. 67, no. 20, pp. 5239-5269, Oct. 2019.
An introduction to matrix concentration inequalities, Joel Tropp, Foundations and Trends® in Machine Learning, 2015.