Computation and optimization for machine learning

2024/2025

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

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

Course type:

Elective course

When:

2 year, 1, 2 module

Instructor

Nozdrinova, Elena

Course Syllabus

Abstract

Course starts with a basic introduction to concepts concerning functional mappings. Later students are assumed to study limits (in case of sequences, single- and multivariate functions), differentiability (once again starting from single variable up to multiple cases), integration, thus sequentially building up a base for the basic optimisation. To provide an understanding of the practical skills set being taught, the course introduces the final programming project considering the usage of optimisation routine in machine learning.Additional materials provided during the course include interactive plots in GeoGebra environment used during lectures, bonus reading materials with more general methods and more complicated basis for discussed themes

Learning Objectives

• Here we introduce basic concept the calculus course could not be imagine without: function. In order to properly do it, one should say that the function is a mapping from one set to another. Thus, we start with the ideas of numerical sets and mapping, then proceeding with functions itself. Since we are particularly interested in functions' graph, we spend a lot of time discussing simplest ways to produce a complex function graph from elementary case. In the second part of the week we start our calculus journey with a discrete limit, the limit of sequences, and master skills needed to calculate them.

Expected Learning Outcomes

• Know the definition of the limit
• Know the definition of function
• Know about symptotic comparison of functions
• Know about the slope of the functions

Course Contents

• Introduction: Numerical Sets, Functions, Limits
• Limits and Multivariate Functions
• Derivatives and Linear Approximations: Singlevariate Functions
• Introduction: Numerical Sets, Functions, Limits

Assessment Elements

• Домашнее задание
• Экзамен

Interim Assessment

• 2024/2025 2nd module
  0.5 * Домашнее задание + 0.5 * Экзамен

Bibliography

Recommended Core Bibliography

• Machine learning : a probabilistic perspective, Murphy, K. P., 2012
• Machine learning, Mitchell, T. M., 1997

Recommended Additional Bibliography

• Machine learning : beginner's guide to machine learning, data mining, big data, artificial intelligence and neural networks, Trinity, L., 2019

Authors

• Трехлеб Ольга Юрьевна
• Nozdrinova Elena Viacheslavovna