Delivered at:: Department of Fundamental Mathematics (Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod))

Course type:: Compulsory course

When:: 1 year, 4 module

Instructor

Remizov, Ivan

Full Syllabus

Abstract

The main goal of the course is to explain the main concepts of linear algebra that are used in data analysis and machine learning. Another goal is to improve the student’s practical skills of using linear algebra methods in machine learning and data analysis. You will learn the fundamentals of working with data in vector and matrix form, acquire skills for solving systems of linear algebraic equations and finding the basic matrix decompositions and general understanding of their applicability. This course is suitable for you if you are not an absolute beginner in Matrix Analysis or Linear Algebra (for example, have studied it a long time ago, but now want to take the first steps in the direction of those aspects of Linear Algebra that are used in Machine Learning). Certainly, if you are highly motivated in study of Linear Algebra for Data Sciences this course could be suitable for you as well.

Learning Objectives

The goal of the course is to apply matrix analysis to machine learning. We study the aspects of linear algebra that are used in data Science.

Expected Learning Outcomes

Know methods for finding linear system solutions based on Gaussian exceptions and LU decompositions. Be able to use Python code for matrix calculations.
Know the fundamental concepts of linear algebra, namely: vector spaces, linear independence and basis, matrix rank, properties of a set of solutions for a system of linear equations. Be able to apply this theory to the processing of scanned documents.
Be able to apply the concepts of Euclidean space in the least squares method for finding approximate solutions of linear systems and in the linear regression model based on it. Know the core of the most common linear classifier, called the support vector machine.

Course Contents

Full rank decomposition and systems of linear equations
This section introduces some fundamental concepts of linear algebra, namely: vector spaces, linear independence and basis, matrix rank, and properties of a set of solutions for a system of linear equations. This theory applies to the processing of scanned documents.
Euclidean spaces
The concept of Euclidean space allows you to measure distances and angles in vector spaces. We use these measures in the least squares method to find approximate solutions to linear systems and in the linear regression model based on it. We describe the core of the most common linear classifier, called the support vector machine.
Systems of linear equations and linear classifier
Introduction to multidimensional geometry and matrix algebra, we study methods for finding linear system solutions based on Gaussian exceptions and LU expansions. The methods are illustrated with examples of Python code for matrix calculations.

Assessment Elements

домашние задания
контрольная работа
экзамен

Interim Assessment

Interim assessment (4 module)
0.3 * домашние задания + 0.3 * контрольная работа + 0.4 * экзамен

Bibliography

Recommended Core Bibliography

A Tutorial on Machine Learning and Data Science Tools with Python. (2017). Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.E5F82B62
Bengfort, B., Bilbro, R., & Ojeda, T. (2018). Applied Text Analysis with Python : Enabling Language-Aware Data Products with Machine Learning. Beijing: O’Reilly Media. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=1827695

Recommended Additional Bibliography

Alpaydin, E. (2014). Introduction to Machine Learning (Vol. Third edition). Cambridge, MA: The MIT Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=836612

Master’s Programme 'Mathematics'

Contacts

First Steps in Linear Algebra for Machine Learning