Course syllabus for Bayesian inference and machine learning

Course syllabus adopted 2023-02-07 by Head of Programme (or corresponding).

Overview

  • Swedish nameBayesiansk inferens och maskininlärning
  • CodeTIF385
  • Credits6 Credits
  • OwnerTKTFY
  • Education cycleFirst-cycle
  • Main field of studyEngineering Physics
  • DepartmentPHYSICS
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 57134
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0122 Project 2 c
Grading: UG		 2 c
0222 Examination 4 c
Grading: TH		 4 c
  • 12 Jan 2024 am J
  • 03 Apr 2024 am J
  • 21 Aug 2024 am J

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

- Undergraduate mathematics: Multivariable analysis (MVE035 or equivalent), linear algebra (MVE670 or equivalent), mathematical statistics (TMA321 or equivalent) - Basic programming skills (MVE035 or equivalent). The Python programming language will be used in the course.

Aim

Building on a first course in mathematical statistics this course aims to provide knowledge on Bayesian inference, both in general and in the context of modeling physical systems, and a deeper understanding of modern machine learning. In combination, this knowledge should provide a firm basis for practical applications of statistical models in science.

The course is partly project-based, and the students will learn to develop and structure computer codes for statistical inference and machine learning with scientific applications. Specifically, students will perform physics projects using the Python programming language with relevant open-source libraries.

Learning outcomes (after completion of the course the student should be able to)

  • perform scientific modeling of physical systems by applying the Bayesian paradigm for inference from data.
  • describe fundamental concepts in Bayesian statistics.
  • explain central aspects of Monte Carlo methods and Markov chains, and numerically apply these methods to sample multivariate probability densities;
  • understand and numerically implement several basic algorithms used in data analysis and  machine learning such as linear methods for regression and classification and simple neural networks;
  • use python for practical applications of statistical inference and machine learning methods and to visualize numerical results.
  • maintain a scientific and ethical conduct in the process of collecting, evaluating, and analyzing data and writing computer programs with a particular consideration of gender equality, equal treatment, and diversity.
  • communicate results and conclusions from a scientific data analysis with clarity and the ability to discuss critically.

Content

The course consists of three integrated parts
  1. Bayesian inference  
  2. Machine learning
  3. Stochastic processes and MCMC simulation 
The following subtopics will be covered
  • Bayesian statistics;
  • Central concepts in machine learning;
  • Linear methods for regression and classification;
  • Neural networks;
  • Stochastic processes, Markov chains, Markov chain Monte Carlo (MCMC) simulation, 

Organisation

  • Lectures
  • Supervised exercise classes (also in the computer lab) 
  • Recommended analytical and numerical exercises
  • Numerical projects

Literature

Course compendium. Lecture notes.
Extra course literature will be announced on the course web page.

Examination including compulsory elements

Written exam
Numerical projects

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.