ACIT4510 Statistical Learning Emneplan

The course covers the foundations and recent advances in Machine Learning from the point of view of Statistical Learning Theory. The goal of this course is to provide students with the practical skills to support the theoretical knowledge acquired during the lecture course and the practical intuitions needed to use and develop effective machine learning solutions to challenging problems.

Access to good statistical/data analysis software is paramount. Therefore, we will illustrate the use of the models throughout the course with real implementation.

None

No formal requirements over and above the admission requirements.

The student should have the following outcomes upon completing the course:

Knowledge

Upon successful completion of the course, the student:

• will have a good understanding the different concepts and methods of supervised and unsupervised statistical learning and how to apply them on large data.
• has advanced knowledge of probabilistic formulation of the various learning problems

;

Skills

Upon successful completion of the course, the student:

• can apply different high-dimensional regression techniques on data
• can apply different classification techniques on data
• can apply clustering techniques on data
• can derive learning algorithms for new models and analyze new data with them.
• can apply dimensionality reduction techniques on data

;

General competence

Upon successful completion of the course, the student:

• can apply different predictive models on data and assess their performance
• can use supervised and unsupervised learning in different real life problem

This course is divided into two parts. The first part with focus on covering the principles of Statistical Learning. Different seminars will be given on the different methodological aspects of Statistical learning, mainly, supervised learning and unsupervised learning.

The second part will focus on the students completing a programming project. This is a real data analysis problem, where the student is asked to carry out the analysis using the tools and techniques from the course and hand in a report documenting the steps he has taken in the analysis. The ultimate goal is to build a predictive model.

The project report will consist of at least 25 pages and max 60 pages.

During this part, there may be lectures if needed, but most of the time will be spent on individual supervision of students in lab-sessions.

Practical training

Lab sessions.

The following required coursework must be approved before the student can take the exam:

One mandatory assignment: A project plan document containing a description of the chosen data set, a preliminary research question and suggested tools and method to apply.

The course shall prepare students for master’s degree programmes at universities and university colleges where different types of differential equations is used.

The elective course is initiated provided that a sufficient number of students choose the course.

No requirements over and above the admission requirements.

Grade scale A-F.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student is capable of:

• explaining the concepts of analytic function, ordinary, singular and regular singular points
• using series to solve differential equations
• defining the Laplace transform and derive it's basic properties
• explaining what characterize Fourier series and how they can be used to solve ordinary and partial differential equations
• recognizing and understanding concepts of complex functions
• giving examples of elliptical, parabolic and hyperbolic partial differential equations and how they are solved

Skills

The student is capable of:

• solving higher order linear differential equations with constant coefficients
• using power series and Frobenius series to solve second order linear differential equations with variable coefficients
• manipulate functions of complex variables
• using the Laplace transform to solve non-homogeneous linear differential equations modelling oscillating systems
• determining the Fourier sine series and the Fourier cosine series of symmetrical expansions of non-periodic functions
• solving boundary value problems relating to partial differential equations in closed domains by separation of variables

General competence

The student:

• has acquired good skills in solving ordinary and partial differential equations
• utilizing complex analysis techniques to solve partial differential equations, related to electrical engineering, acoustic and heat transfer

Lectures and exercises. Practical exercises are solved individually with the help of the pre-written compendium with solutions for all exercises and previous exams. At the end of the course, previous exams will be reviewed during the six weekly periods.