• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • А
  • А
  • А
  • А
  • А
Обычная версия сайта

High-dimensional Statistical Methods

2019/2020
Учебный год
ENG
Обучение ведется на английском языке
6
Кредиты
Статус:
Курс обязательный
Когда читается:
1-й курс, 3 модуль

Преподаватель

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

  • 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

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

Assessment Elements

  • non-blocking Home assignment 1
  • non-blocking Home assignment 2
  • non-blocking Final written test
    Оценка за дисциплину выставляется в соответствии с формулой оценивания от всех пройденных элементов контроля. Экзамен не проводится.
Interim Assessment

Interim Assessment

  • Interim assessment (3 module)
    0.2 * Final written test + 0.4 * Home assignment 1 + 0.4 * Home assignment 2
Bibliography

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.