Mathematical Methods for Data Analysis

2024/2025

Academic Year

ENG

Instruction in English

5

ECTS credits

Delivered at:

Big Data and Information Retrieval School

Course type:

Compulsory course

When:

3 year, 1, 2 module

Instructors

Bykov, Kirill

Горбунов Иван Игоревич

Lazarev, Mikhail

Сулеев Дамир Ранилевич

Червяков Артем Александрович

Course Syllabus

Abstract

This course presents the foundations of rapidly developing scientific field called intellectual data analysis or machine learning. This field is about algorithms that automatically adjust to data and extract valuable structure and dependencies from it. The automatic adjustment to data by machine learning algorithms makes it especially convenient tool for analysis of big volumes of data, having complicated and diverse structure which is a common case in modern "information era". During this course most common problems of machine learning are considered, including classification, regression, dimensionality reduction, clustering, collaborative filtering and ranking. The most famous and widely used algorithms suited to solve these problems are presented. For each algorithm its data assumptions, advantages and disadvantages as well as connections with other algorithms are analyzed to provide an in-depth and critical understanding of the subject. Much attention is given to developing practical skills during the course. Students are asked to apply studied algorithms to real data, critically analyze their output and solve theoretical problems highlighting important concepts of the course. Machine learning algorithms are applied using python programming language and its scientific extensions, which are also taught during the course. The course is designed for students of the bachelor program "Software Engineering" at the Faculty of Computer Science, HSE.

Learning Objectives

• distinguish major problems of data analysis, solved with machine learning
• recognise and be able to apply major algorithms to solve stated problems
• understand and be able to reproduce core machine learning algorithms
• understand dependencies between algorithms, their advantages and disadvantages
• be able to use data analysis libraries from python - numpy, scipy, pandas, matplotlib and scikit-learn
• understand, which kinds of algorithms are more appropriate for what kinds of data
• know, how to transform data to make it more suitable for machine learning algorithms

Expected Learning Outcomes

• Can derive updates for kmeans
• Can state and explain one-class SVM optimization problem
• To be able to explain why error rate cannot be used in gradient training of a classifier
• To be familiar with key objects of the course
• To formulate and statistical concepts: bootstrap, bias, variance
• To formulate optimization objective for logistic Regression and SVM

Course Contents

• Introduction to Machine Learning
• Basic gradient optimization
• Linear Regression Model
• Linear Classification
• Logistic Regression and SVM
• Decision Trees
• Bagging, Random Forest and Bias-Variance Tradeoff
• Gradient boosting
• Clustering and Anomaly Detection
• Dimensionality reduction: PCA, SVD
• Testing your model: AA/AB tests
• From MultiLayer Perceptron to Deep Neural Networks
• Machine Learning: Business Applications
• Summary
• Introduction to NLP & LLM

Assessment Elements

• Экзамен
• Домашние задания
  ДЗ — средняя оценка за все домашние задания

Interim Assessment

• 2024/2025 2nd module
  0.7 * Домашние задания + 0.3 * Экзамен

Bibliography

Recommended Core Bibliography

• Christopher M. Bishop. (n.d.). Australian National University Pattern Recognition and Machine Learning. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.EBA0C705
• Trevor Hastie, Robert Tibshirani , et al., The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edition, 2017. Free from the publisher: https://web.stanford.edu/~hastie/ElemStatLearn/printings/ESLII_print12.pdf

Recommended Additional Bibliography

• Mehryar Mohri, Afshin Rostamizadeh, & Ameet Talwalkar. (2018). Foundations of Machine Learning, Second Edition. The MIT Press.

Authors

• Сысоева Алевтина Александровна