Магистратура 2020/2021

Современные методы принятия решений: Современные статистические методы

Статус: Курс обязательный (Математика машинного обучения)

Направление: 01.04.02. Прикладная математика и информатика

Кто читает: Кафедра технологий моделирования сложных систем

Где читается: Факультет компьютерных наук

Когда читается: 1-й курс, 3 модуль

Формат изучения: без онлайн-курса

Преподаватели: Спокойный Владимир Григорьевич

Прогр. обучения: Статистическая теория обучения

Язык: английский

Кредиты: 6

Контактные часы: 32

Course Syllabus

Abstract

The course «Modern Methods in Decision Making» is a course taught in the first year of the Master’s program «Data Science». It is compulsory for all students of the Master’s program. The course is in the continuation of the core course «Modern methods of Data Analysis» proposed in Modules 1 and 2 in the Master`s program «Data Science». Students are expected to be already familiar with some statistical learning techniques, and have skills in analysis, linear algebra and probability theory. Students must have completed the course «Probability Theory and Mathematical Statistics».

Learning Objectives

• The student is able to reflect developed mathematical models in statistical learning.
• The student is able to select a model using validation techniques and to test it on dataset from coming from reallife examples.
• Students obtain necessary knowledge in statistical learning, sufficient to develop and understand new methods in closely related disciplines such a s i n M a c h i n e Learning.

Expected Learning Outcomes

• Essential basis for working with complex data structures using modern statistical tools

Course Contents

• Validation techniques
  Akaike Information Criteria, Bayesian Information Criteria, Cross-Validation.
• Ensemble Methods
  Bagging, Random Forests, Convex Relaxation, Boosting, AdaBoost, Gradient Boosting.
• Elements of Vapnik-Chervonenkis Theory
  Bounds on the estimation error, Vapnik-Chervonenkis inequality, Vapnik-Chervonenkis dimension, Structural Risk Minimization.
• Tree-based models
  Classification and Regression Trees (CART).
• Support Vector Machine
  Elements of Convex Optimization, Kernels, Reproducible Kernel Hilbert Spaces.
• Linear Classifiers
  Logistic regression, Linear Discriminant Analysis.
• Probabilistic Approach to Pattern Recognition.
  Loss function, Risk, Bayes estimator, Empirical Risk Minimization, Bias-Variance Tradeoff, Approximation and Estimation Error.
• Linear regression techniques
  Multivariate Linear Regression, Ridge regression, Lasso, Elastic-net.
• Polynomial regression and splines
  Polynomial regression, splines, natural spline, smoothing splines.

Assessment Elements

• Mid-Term Exam
• Homework
• Exam
  Оценка за дисциплину выставляется в соответствии с формулой оценивания от всех пройденных элементов контроля. Экзамен не проводится.

Interim Assessment

• Interim assessment (3 module)
  0.5 * Exam + 0.25 * Homework + 0.25 * Mid-Term Exam

Bibliography

Recommended Core Bibliography

• Gareth James, Daniela Witten, Trevor Hastie, Rob Tibshirani, & Maintainer Trevor Hastie. (2013). Type Package Title Data for An Introduction to Statistical Learning with Applications in R Version 1.0. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.28D80286
• Hastie, T., Tibshirani, R., & Friedman, J. H. (2009). The Elements of Statistical Learning : Data Mining, Inference, and Prediction (Vol. Second edition, corrected 7th printing). New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=277008

Recommended Additional Bibliography

• James, G. et al. An introduction to statistical learning. – Springer, 2013. – 426 pp.
• Trevor Hastie, Robert Tibshirani, & Jerome Friedman. New York. (n.d.). Book Reviews 567 The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.45E1D521