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.