This module will introduce the students to a selection of techniques and theoretical concepts related to multivariate data analysis. The first part of the module will be devoted to the study of some basic notions in multivariate probability, with a special emphasis on the multivariate Gaussian distribution. The conditioning of Gaussian vectors will then be used to introduce the kernel-regression framework, and the second part of the module will thus consist of an introduction to kernel methods, which form an important class of techniques in machine learning and mathematical modelling. The third part of the module will focus on some classical topics in multivariate statistics.

The students will acquire an advanced theoretical understanding of the underlying mathematical concepts; they will in parallel develop their scientific programming and technical writing skills. The students will have the opportunity to use either R or Python to complete the computational component of the module. 

• Understand the foundations of multivariate probability and statistics.
• Perform computations involving random vectors and random matrices.
• Implement and apply some kernel regression models.
• Handle multivariate data.  

Modules will be delivered through blended learning. You will be guided through learning activities appropriate to your module, which may include:

• Weekly face to face classes (e.g. labs, lectures, exercise classes)
• Electronic resources that you work through at your own pace (e.g. videos, exercise sheets, lecture notes, e-books, quizzes)

Students are also expected to undertake self-guided study throughout the duration of the module.

Skills that will be practised and developed:

• Perform computations in the multivariate setting.
• Probability and statistics.
• Scientific programing and technical writing.
• Kernel methods.
• Connections between data science and mathematics.

Transferable Skills:

• Handling multivariate data.
• Performing computations in the multivariate setting.
• Understanding of the theoretical foundations of some multivariate data-analysis techniques.  
• Introduction to kernel methods.
• Scientific programing.
• Technical/scientific writing.  

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.  

• Multivariate random variables.
• Conditioning of Gaussian random vectors.  
• Kernel regression.  
• Multivariate statistics.  
• Scientific programming in R or Python.