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Магистратура 2023/2024

# Вероятность и статистика в высокой размерности

Лучший по критерию «Новизна полученных знаний»
Статус: Курс обязательный (Математика машинного обучения)
Направление: 01.04.02. Прикладная математика и информатика
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

#### Assessment Elements

• Home assignment 1
• Home assignment 2
• Final written test

#### Interim Assessment

• 2023/2024 4th module
0.2 * Final written test + 0.4 * Home assignment 1 + 0.4 * Home assignment 2

#### Recommended Core Bibliography

• Concentration inequalities : a nonasymptotic theory of independence, Boucheron, S., 2013

#### Recommended Additional Bibliography

• Elements of information theory, Cover, T. M., 2006

#### Authors

• YAKOVLEVA ILONA ALEKSANDROVNA