ELE538: Mathematics of High-Dimensional Data

Textbooks. We recommend the following books, although we will not follow them closely.

• High-dimensional data analysis with sparse models: Theory, algorithms, and applications, John Wright, Yi Ma, Allen Yang, 2018.

• Statistical machine learning for high-dimensional data, Jianqing Fan, Runze Li, Cun-Hui Zhang, Hui Zou, 2018.

• High-dimensional statistics: A non-asymptotic viewpoint, Martin J. Wainwright, 2019.

• 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.

• An Introduction to Matrix Concentration Inequalities, Joel Tropp, Foundations and Trends in Machine Learning, 2015.

• Mathematics of sparsity (and a few other things), Emmanuel Candes, International Congress of Mathematicians, 2014.

• Sparse and redundant representations: from theory to applications in signal and image processing, Michael Elad, Springer, 2010.

• Graphical models, exponential families, and variational inference, Martin Wainwright, and Michael Jordan, Foundations and Trends in Machine Learning, 2008.

• Introduction to the non-asymptotic analysis of random matrices, Roman Vershynin, Compressed Sensing: Theory and Applications, 2010.

• Convex optimization, Stephen Boyd, and Lieven Vandenberghe, Cambridge University Press, 2004.

• Topics in random matrix theory, Terence Tao, American Mathematical Society, 2012.

• Statistical learning with sparsity: the Lasso and generalizations, Trevor Hastie, Robert Tibshirani, and Martin Wainwright, Chapman and Hall/CRC, 2015.

• A mathematical introduction to compressive sensing, Simon Foucart, and Holger Rauhut, Springer, 2013.