Module MATH4287: High-Dimensional Statistics

Department: Mathematical Sciences

MATH4287: High-Dimensional Statistics

Prerequisites

• Statistical Inference (MATH2711)

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• To provide advanced methodological skills for the analysis of high-dimensional data, spanning the arc from the theoretical underpinning of the methods to the practical application on real data.

Content

• Introduction to high-dimensional statisics
• Dimension reduction: regularized regression techniques such as lasso, ridge, elastic net, and more advanced techniques.
• Multivariate statistics: principal component analysis, cluster analysis, and related methods.
• R packages for implementation of the methods.

Learning Outcomes

• A thorough understanding and working knowledge of advanced statistical methods for multivariate data;
• An appreciation of the wider concepts that such methods are built on, allowing straightforward understanding of yet unseen methods;
• The intuition to distinguish supervised and unsupervised learning scenarios, and which specific methods to apply in particular situations.

• Students will have advanced mathematical skills in the following areas: modelling, computation.

• Students will have advanced skills in the following areas: problem solving, synthesis of data, critical and analytical thinking, report writing.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Computer practicals consolidate the studied material, explore theoretical ideas in practice, enhance practical understanding, and develop practical data analysis skills.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formative assessments provide feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
• The written project report assesses the ability to implement the concepts introduced in the module using statistical software, to apply them in the analysis of a realistic problem, and to report scientific outputs in a clear and structured way.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Two assignments to be submitted.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University