MA3506: Multivariate Data Analysis

School Cardiff School of Mathematics
Department Code MATHS
Module Code MA3506
External Subject Code 100406
Number of Credits 10
Level L6
Language of Delivery English
Module Leader DR Bertrand Gauthier
Semester Spring Semester
Academic Year 2018/9

Outline Description of Module

This module introduces techniques and theoretical concepts related to multivariate data analysis. The first part of the module focuses on classical multivariate statistics topics, with a particular emphasis on the properties of the sample mean and covariance estimators related to multivariate datasets, and on the properties of the multivariate Gaussian distribution. The second part of the module focuses on dimension reduction, random-field models and kernel-based technics for multivariate data analysis. The main goal of the module is to help the students to acquire a good theoretical understanding of the underlying mathematical concepts, and to develop skills in handling, analysing and modelling multivariate problems.  

On completion of the module a student should be able to

  • Handle random vectors and random matrices.
  • Understand the foundation of some modern data analysis methods.
  • Implement and apply various multivariate learning techniques.

How the module will be delivered

20 fifty-minute lectures

7 fifty-minute computer laboratory lectures

Lecture notes will be provided in hard copy and via Learning Central, but students are expected to take additional notes during the lectures.

Students are also expected to undertake private study including preparation of solutions to given exercises.

Skills that will be practised and developed

Performing computations involving multivariate random elements; understanding the properties of the multivariate Gaussian distribution and the foundations of modern data-analysis techniques; handling, analysing and modelling multivariate datasets. 

Transferable Skills:
Handling and analysing high dimensional data; performing computations involving multivariate random elements; knowledge of the foundations of modern multivariate data-analysis techniques.

How the module will be assessed

Formative assessment is carried out by means of homework, and feedback to the students is provided during exercise lectures and lab sessions.

The major component of summative assessment is a written examination at the end of the module. which gives students the opportunity to demonstrate their overall understanding of the notions taught during the module. The examination paper has a choice of three from four equally weighted questions.

The summative assessment also includes a coursework (or “mini project”) that is completed by the students during the last part of the module, and which is assessed through the production of a small report; this gives the students the opportunity to demonstrate their theoretical and technical knowledge while developing their scientific writing and synthesis skills.  

Assessment Breakdown

Type % Title Duration(hrs)
Exam - Spring Semester 75 Multivariate Data Analysis 2
Written Assessment 25 Coursework N/A

Syllabus content

  • Random vectors and matrices
  • Multivariate distributions
  • Gaussian random vectors
  • Dimension reduction
  • Random-field models and kernel-based methods

Background Reading and Resource List

Bilodeau, M. and Brenner, D. (1999) Theory of Multivariate Statistics, Springer-Verlag, NY.

Rasmussen, C.E. and Williams, C.K.I (2006), Gaussian Processes for Machine Learning. The MIT Press.eBook available via http://bit.ly/2w1UAvn

Anderson, T. W.  (2003) An Introduction to Multivariate Statistical Analysis, Wiley, Hoboken, NJ.


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