High-dimensional Statistical Methods
- Understand the effect of dimensionality on the performance of statistical methods
- Popular methods adapted to the high-dimensional setting
- knowledge of what a sub-gaussian random variable is.
- Understanding the behaviour of suprema of random variables
- BIC, LASSO and SLOPE methods for high-dimensional linear regression
- Knowledge of basic probabilistic results related to random matrices and useful in statistics.
- Сoncentration of sums of independent random variablesSubgaussian distributions; Subgamma distributions.
- SupremaFinite case; Suprema over convex polytopes; Covering and packing numbers; Chaining bounds.
- High dimensional regressionBIC, LASSO and SLOPE estimators.
- Statistics and random matricesAnalysis and probability with matrices; Matrix version of Bernstein’s inequality; High dimensional PCA and random projections.
- Interim assessment (3 module)0.2 * Final written test + 0.4 * Home assignment 1 + 0.4 * Home assignment 2
- Boucheron, S., Lugosi, G., Massart, P. Concentration inequalities: A nonasymptotic theory of independence. – Oxford university press, 2013.
- Cover, Thomas M., Thomas, Joy A. Elements of information theory. – Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. – 774 pp.