Unit information: Advanced Linear Modelling and Classification in 2024/25

Unit name	Advanced Linear Modelling and Classification
Unit code	MATH20016
Credit points	20
Level of study	I/5
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
Unit director	Professor. Andrieu
Open unit status	Not open
Units you must take before you take this one (pre-requisite units)	MATH10013 Probability and Statistics, MATH10016 Matrix Algebra and Linear Models
Units you must take alongside this one (co-requisite units)	MATH20800 Statistics
Units you may not take alongside this one	None
School/department	School of Mathematics
Faculty	Faculty of Science

Unit Information

Why is this unit important?

Statistical regression and classification methods are ubiquitous in modern Data Science, and it is therefore important that students obtain an overview of this area at a relatively early stage of their studies. In particular, they will encounter important concepts such as overfitting, bias-variance trade-off, shrinkage, basis expansions and random effects which permeate many advanced modelling and classification techniques, and to acquire experience in applying a range of regression and classification techniques. This unit complements the more detailed foundational training provided by Probability 2 and Statistics 2, by showing how those foundations translate to modern data analytic tools.

How does this unit fit into your programme of study?

The unit builds on earlier more foundational statistical courses and aims to provide a more practical experience by focussing on a class of models which forms the nuts and bolts of a variety of standard applications. Principles and theory of linear modelling and its classical extensions are covered in lectures and an emphasis is put on applying these ideas to real datasets using standard statistical libraries. At the end of the unit students will be able to use R libraries and interpret with confidence the output of their standard functions in order conduct proper prediction tasks.

Your learning on this unit

An overview of content

The unit aims to provide students with an overview of modern regression and classification methods and skills to use relevant R packages to analyse simple datasets.

Topics will include:

• An overview of regression and classification,
• Generalised linear models, maximum likelihood estimation and random effects,
• Classification: KNN, linear discriminant analysis and Logistic regression,
• Model diagnosis,
• Model assessment and selection (Bias-variance trade-off, overfitting, subset selection,
  

resampling methods, regularisation.)

• Basis expansions, local regression, generalised additive models,
  

Introduction to kernel-based methods,

• Associated computing (R functions lm, glm, lda, knn, loess, R packages mgcv, glmnet, splines).

How will students, personally, be different as a result of the unit

After the unit students will know how to apply multilinear regression, and its variations, to real datasets using standard R libraries and will be able to interpret their output with confidence.

Learning Outcomes

By the end of the course, students should be able to:

• Identify appropriate regression or classification methods when presented with applied problems requiring their use.
• Use and critically assess a range of modern regression and classification methods.
• Perform model diagnosis and model selection.
• Demonstrate understanding of how the methods covered in the unit work.
• Demonstrate the ability to use the methods in R, and to interpret the results appropriately.
• Demonstrate an understanding of the relationship between the methods and models taught, and of their relative strengths and weaknesses

How you will learn

Learning will be through a combination of the following:

• Problem sheets with a combination of programming tasks completed in Python and more mathematical questions;
• Lectures with active participation;
• Computer labs where students will work on problems;
• Reading recommended books to strengthen understanding.

How you will be assessed

Tasks which help you learn and prepare you for summative tasks (formative):

There will be unassessed problem sheets and practice computer practical to be completed through a combination of programming tasks completed in R and more mathematical questions.

Tasks which count towards your unit mark (summative):

This unit will be assessed through a final 1.5 hour exam (80%) and summative coursework (20%).

When assessment does not go to plan

Students who do not take or pass the final exam in the first round will typically complete a resit.
Students will only be able to retake the summative coursework in exceptional circumstances.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH20016).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the University Workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.