Aims

To develop an understanding of the statistical theory underpinning methods and models for the analysis of “big” and, in particular, multivariate data. To gain experience in the application of this theory to a large data set.

Module summary

More data than ever before are being generated and stored, in a variety of fields such as healthcare and e-commerce. The term “big data” has emerged in acknowledgement of the vast amounts of data now available. By applying statistical analyses to these data sets, we can start to use them to answer important questions, for example, which genetic markers are associated with incidence of a particular disease. Commonly the data sets that arise are multivariate, comprising a large number of observations on many variables. In this module we study how we can learn from data sets of this form. We begin by considering their representation in R, and techniques for generating numerical and graphical summaries. We then turn to consider more formal techniques - often branded "unsupervised learning" - intended to summarise the relationships between variables or observations. Finally we consider a collection of inferential procedures - so-called "supervised learning" techniques - where the goal is to predict a categorical or quantitative response variable on the basis of a collection of covariates. In the latter case, we study linear regression, focusing on overcoming the problems that arise when confronted with a very large number of covariates.

Outline Of Syllabus

Introduction to big data, particularly multivariate data, data summaries and use of R data frames. Principal components and cluster analysis. Classification methods using discriminant analysis; use of cross-validation. Methods based on linear regression, including variable selection methods; shrinkage using ridge regression, the lasso and the elastic net; dimension reduction using principal components regression and partial least squares.

Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.