Магистратура
2023/2024
Вероятность и статистика в высокой размерности
Статус:
Курс обязательный (Математика машинного обучения)
Направление:
01.04.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
1-й курс, 3, 4 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для своего кампуса
Прогр. обучения:
Математика машинного обучения
Язык:
английский
Кредиты:
6
Контактные часы:
80
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
