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# Modern Methods of Decision Making: Advanced Statistical Methods

2019/2020
Учебный год
ENG
Обучение ведется на английском языке
3
Кредиты
Статус:
Курс обязательный
Когда читается:
1-й курс, 3, 4 модуль

### 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
• 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 (4 module)
0.5 * Exam + 0.25 * Homework + 0.25 * Mid-Term Exam

#### 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