Mathematics for Machine Learning, 7.5 credits

Main field of study with advanced study

English 6 and the course Linear Algebra for Data Science 7.5 credits. Exemption of the requirement in Swedish is granted.

The course is offered in the programme Applied Artificial Intelligence (A1) 180 hp. The course is also given as a single subject course.

The aim of the course is for students to learn to practically apply the multivariate calculus utilized in many common machine learning techniques. The students will develop intuitive understanding of calculus using visualization means and concepts’ instantiation to make them more tangible. Exercises and applications are developed in Python that contains numerical and visualization libraries. The students will be able to apply theoretical knowledge of calculus into training models such as linear regression and neural networks.

Following successful completion of the course the student should be able to:

Knowledge and understanding

• explain how derivatives and gradients are used to understand the growth rate of functions
• describe how functions can be approximated with power series
• explain how functions can be used to fit data

Skills and ability

• derivate multivariate functions and calculate gradients, Jacobians and Hessians
• approximate functions using Taylor series
• find minima and maxima of multivariate functions using gradient descent
• fit a function to data using models including linear regression and neural networks

Judgement and approach

• quantitatively judge the accuracy of a function approximation
• judge the complexity of a function and elaborate appropriate approximation and optimization needed for a given problem
• identify the need of further knowledge in the subject and the applicability of multivariate calculus to optimization problems

The course contains multiple topics in calculus and multivariate calculus which are utilized in and are fundamental to many machine learning methods as: functions, gradients, derivatives, derivation rules, functions of many variables, partial derivatives, the Jacobian, multivariate chain rule and application to neural networks, approximation of functions, power series, multivariate Taylor series, optimization, gradient descent and regression.

The teaching includes lectures, computer labs and project supervision.

The teaching is given in English.

The course is examined through a written individual classroom examination. The course is also examined through laboratory work and a project for which the student can choose to do individually or in a group.

The final course grade is the weighted average of the grades on the written Examination and project. However, all parts must be successfully completed in order to pass the course. For grade 4, it is required that the average is greater than or equal to 3,5 and approved laboratory work. For grade 5, it is required that the average is greater than or equal to 4,5 and approved laboratory work.

If there are special reasons, the examiner may make exceptions from the specified examination format and allow a student to be examined in another way. Special reasons can e.g. be study support for students with disabilities.

Course evaluation is part of the course. This evaluation offers guidance in the future development and planning of the course. Course evaluation is documented and made available to the students.S