Machine Learning B (MLB)

Course content

The course is a continuation of Machine Learning A course and provides deeper theoretical foundations of machine learning and a number of advanced theoretically grounded learning techniques. Tentative list of topics includes:

  • Basics in Optimization Theory
    • Basic properties of functions: convexity, Lipschitzness, gradients, subgradients, etc.
    • Constrained optimization and the method of Lagrange multipliers
    • Stochastic Gradient Descent (SGD)
    • Convergence proof for SGD
    • Alternating optimization methods
  • Basics of Information Theory
    • Entropy
    • Relative entropy (the Kullback-Leibler divergence)
    • The method of types
    • kl inequality for concentration of measure
  • Advanced techniques for analysing generalisation power of learning algorithms
    • Vapnik-Chervonenkis (VC) analysis
    • VC analysis of SVMs
    • VC lower bound
    • PAC-Bayesian analysis
    • PAC-Bayesian analysis of majority vote
    • Bernstein-type concentration inequalities, with applications to analysis of learning algorithms
  • Kernel Methods
    • Kernels and RKHS
    • SVMs
  • Ensemble classifiers and weighted majority vote
    • Boosting
  • Bayesian inference
    • Difference between Bayesian and frequentist views


WARNING: The course assumes that you have taken DIKU's Machine Learning A course. If you have not taken it, please, carefully check the "Recommended Academic Qualifications" box below and the self-preparation assignment at Machine Learning courses given at other places do not necessarily prepare you well for this course. It is not advised taking the course if you do not meet the academic qualifications.


Physical & Online: This is a physical course, but we support remote participation.


BSc Programme in Machine Learning and Data Science
MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics-Economics
MSc Programme in Computer Science
MSc Programme in Computer Science (part time)
MSc Programme in Computer Science (with minor subject)
MSc Programme in Statistics

Learning outcome

At course completion, the successful student will have:

Knowledge of

  • advanced understanding of the concept of generalisation;
  • advanced tools for analysis of generalisation power of machine learning algorithms;
  • the mathematical foundations of selected advanced machine learning algorithms.


Skills in

  • deriving advanced generalisation bounds for expected prediction quality;
  • applying advanced linear and non-linear techniques for classification and regression;
  • implementing selected advanced machine learning algorithms;
  • visualising and evaluating results obtained with machine learning techniques;
  • using software libraries for solving machine learning problems.


Competences in

  • recognising and describing possible applications of machine learning;
  • formalising and rigorously analysing machine learning problems;
  • comparing, appraising and selecting machine learning methods for specific tasks;
  • solving real-world data mining and pattern recognition problems by using machine learning techniques.

Weekly lectures, weekly home assignments, exercise classes

Will be published on Absalon.

It is assumed that the students have successfully passed Machine Learning A course. Machine Learning courses given at other places do not necessarily prepare you well for this course.
Please, check the self-preparation assignment at https:/​/​​​machine-learning-courses/​ml-b.

The course requires strong mathematical skills and background corresponding to what is achieved on the BSc. in Machine Learning and Data Science. In particular:

1. Knowledge of Linear Algebra corresponding to Lineær algebra i datalogi course (LinAlgDat)

2. Knowledge of Calculus corresponding to Introduktion til matematik i naturvidenskab (MatintroNat) or Matematisk analyse og sandsynlighedsteori i datalogi (MASD).

3.Knowledge of Probability Theory corresponding to Sandsynligheds-regning og statistik (SS), Grundlæggende statistik og sandsynlighedsregning (GSS) or Matematisk analyse og sandsynlighedsteori i datalogi (MASD) and Modelling analysis of data (MAD).

4.Knowledge of Discrete Mathematics corresponding to Diskret matematik og formelle sprog (DMFS) or Diskret Matematik og algoritmer (DMA).

5. Knowledge of programming corresponding to Programmering og problemløsning (PoP) and experience with programming in Python.

The course is similar to NDAB21008U Machine Learning B (MLB). Students who have previously passed NDAB21008U Machine Learning B (MLB) are not al-lowed to sign up for this course."

Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Written assignment, 75 hours
Type of assessment details
The exam is a written take-home assignment (must be solved individually).
*Please note: that the planned exam workload is 25 hours. We provide extra days to allow the students to combine the exam with other potential duties, such as other exams or work commitments
Exam registration requirements

5-7 mandatory written take-home assignments (must be solved individually).

A student must score above 50% on average in the assignments in order to qualify for the exam. 

All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship

Same as the ordinary exam.

Prerequisite for participation in the re-exam is handing in the course assignments no later than 3 weeks prior to the re-exam week and scoring at least 50% on average in these assignments.

Criteria for exam assessment

See Learning Outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 34
  • Preparation
  • 8
  • Theory exercises
  • 57
  • Practical exercises
  • 57
  • Exam Preparation
  • 25
  • Exam
  • 25
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 2
No limit.
The number of seats may be reduced in the late registration period
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Computer Science
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Sadegh Talebi   (13-766467686a6b3177646f68656c43676c316e7831676e)

Yevgeny Seldin, Christian Igel & Sadegh Talebi

Saved on the 26-05-2023

Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students