Master
2020/2021
High-dimensional Statistical Methods
Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type:
Compulsory course (Statistical Learning Theory)
Area of studies:
Applied Mathematics and Informatics
Delivered by:
School of Data Analysis and Artificial Intelligence
Where:
Faculty of Computer Science
When:
1 year, 3 module
Mode of studies:
offline
Instructors:
Quentin Paris
Master’s programme:
Statistical Learning Theory
Language:
English
ECTS credits:
6
Contact hours:
32
Course Syllabus
Abstract
The course presents an introduction to modern statistical and probabilistic methods for data analysis, emphasising finite sample guarantees and problems arising from high-dimensional data. The course is mathematically oriented and level of the material ranges from a solid undergraduate to a graduate level. Topics studied include for instance Concentration Inequalities, High Dimensional Linear Regression and Matrix estimation. Prerequisite: Probability Theory.
Learning Objectives
- Understand the effect of dimensionality on the performance of statistical methods
- Popular methods adapted to the high-dimensional setting
Expected Learning Outcomes
- 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.
Course Contents
- 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.
Assessment Elements
- Home assignment 1
- Home assignment 2
- Final written testОценка за дисциплину выставляется в соответствии с формулой оценивания от всех пройденных элементов контроля. Экзамен не проводится.
Interim Assessment
- Interim assessment (3 module)0.2 * Final written test + 0.4 * Home assignment 1 + 0.4 * Home assignment 2
Bibliography
Recommended Core Bibliography
- Boucheron, S., Lugosi, G., Massart, P. Concentration inequalities: A nonasymptotic theory of independence. – Oxford university press, 2013.
Recommended Additional Bibliography
- Cover, Thomas M., Thomas, Joy A. Elements of information theory. – Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. – 774 pp.