High Dimension Statistics

Basic information

Workload: 

45 hours

Prerequisite: 

Mathematical Statistics, Foundations of Machine Learning.
 

Syllabus: 

Sub-Gaussian and sub-exponential random variables; Chernoff Bounds; Maximal inequalities; Restricted least squares; Regularization and sparse; high-dimensional linear regression; Oracle Inequalities; Non-parametric estimation; Estimation of covariance matrices; principal component analysis; Minimax optimality; relationship with hypothesis testing and lower quotas.

Bibliography

Mandatory: 

·       Koltchinskii, V. (2008) Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems.
·       Massart, P. (2007). Concentration inequalities and model selection (Vol. 6). Berlin: Springer..
·       Rigollet, P. (2015). High-dimensional statistics. Lecture notes for course 18S997.

Complementary: 

·       Giraud, C. (2014). Introduction to high-dimensional statistics(Vol. 138). CRC Press.
·       Devroye, L., Györfi, L., & Lugosi, G. (2013). A probabilistic theory of pattern recognition (Vol. 31). Springer Science & Business Media.
·       Bühlmann, P., & Van De Geer, S. (2011). Statistics for high-dimensional data: methods, theory and applications. Springer Science & Business Media.
·       Vershynin, R. (2016). High-Dimensional Probability An Introduction with Applications in Data Science.
·       Tibshirani, R., Wainwright, M., & Hastie, T. (2015). Statistical learning with sparsity: the lasso and generalizations. Chapman and Hall/CRC.