High-dimensional Statistical Methods

2019/2020

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Департамент анализа данных и искусственного интеллекта

Статус:

Курс обязательный

Когда читается:

1-й курс, 3 модуль

Преподаватель

Пари Кентан Поль Бернар

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

Bibliography

Recommended Core Bibliography

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

Recommended Additional Bibliography

• Cover, Thomas M., Thomas, Joy A. Elements of information theory. – Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. – 774 pp.