• A
• A
• A
• ABC
• ABC
• ABC
• А
• А
• А
• А
• А
Regular version of the site
Master 2019/2020

High-dimensional Statistical Methods

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
When: 1 year, 3 module
Mode of studies: offline
Instructors: Quentin Paris
Master’s programme: Statistical Learning Theory
Language: English
ECTS credits: 6

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 variables
Subgaussian distributions; Subgamma distributions.
• Suprema
Finite case; Suprema over convex polytopes; Covering and packing numbers; Chaining bounds.
• High dimensional regression
BIC, LASSO and SLOPE estimators.
• Statistics and random matrices
Analysis 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 test
Оценка 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 Recommended Core Bibliography

• Boucheron, S., Lugosi, G., Massart, P. Concentration inequalities: A nonasymptotic theory of independence. – Oxford university press, 2013.