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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

Learning Objectives

  • Understand the effect of dimensionality on the performance of statistical methods
  • Popular methods adapted to the high-dimensional setting
Expected Learning Outcomes

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

Course Contents

  • Сoncentration of sums of independent random variables
  • Suprema
  • High dimensional regression
  • Statistics and random matrices
Assessment Elements

Assessment Elements

  • non-blocking Home assignment 1
  • non-blocking Home assignment 2
  • non-blocking Final written test
Interim Assessment

Interim Assessment

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

Bibliography

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