Master
2024/2025
High Dimensional Probability and Statistics
Type:
Compulsory course (Math of Machine Learning)
Area of studies:
Applied Mathematics and Informatics
Delivered by:
Big Data and Information Retrieval School
Where:
Faculty of Computer Science
When:
1 year, 3, 4 module
Mode of studies:
offline
Open to:
students of one campus
Master’s programme:
Math of Machine Learning
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
- BIC, LASSO and SLOPE methods for high-dimensional linear regression
- Knowledge of basic probabilistic results related to random matrices and useful in statistics.
- knowledge of what a sub-gaussian random variable is.
- Understanding the behaviour of suprema of random variables
Course Contents
- Сoncentration of sums of independent random variables
- Suprema
- High dimensional regression
- Statistics and random matrices
Interim Assessment
- 2024/2025 4th module0.2 * Final written test + 0.4 * Home assignment 1 + 0.4 * Home assignment 2
