ACM41020 Maths of Machine Learning

The aim of this course is to introduce Machine Learning from the point of view of modern optimisation and approximation theory.

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Curricular information is subject to change

Learning Outcomes:

By the end of the module the student should be able to:
- Describe the problem of machine learning from the point of view of function approximation, optimisation, linear algebra, and statistics.
- Identify the most suitable approach for a given machine learning problem.
- Analyse the performance of various machine learning algorithms from the point of view of computational complexity and statistical accuracy.
- Implement a simple neural network architecture and apply it to a pattern recognition task.

Indicative Module Content:

Material will cover the following mathematical topics relevant to Machine Learning:

Highlights from Linear Algebra
- Matrix multiplication
- The four fundamental subspaces
- Types of Matrix
- Matrix factorisation
- Eigenvalues and eigenvectors
- Symmetric, positive definite matrices
- Singular values and singular value decomposition
- Vector and matrix norms

Understanding data
- Linear regression
- Principal component analysis

Support vector machines
- Introduction to support vector machines
- Optimisation
- Lagrange multipliers
- Limitations
- Soft margins
- Kernel trick
- Multiple classes

Neural networks
- Introduction to neural networks
- Activation functions
- Architecture of a neural network
- Training a neural network
- Calculus on computational graphs
- Efficient matrix multiplication
- Backpropagation
- Universal approximation theorem
- Cross-entropy cost function

Optimisation
- Introduction to optimisation
- Newton's method
- Momentum

Student Effort Hours:
Student Effort Type Hours
Lectures

36

Specified Learning Activities

36

Autonomous Student Learning

36

Total

108

Approaches to Teaching and Learning:
Lectures, Problem Classes, Assignments
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
Not applicable to this module.

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Quizzes/Short Exercises: Weekly short quizzes n/a Standard conversion grade scale 40% No

5

Exam (In-person): 2 hour End of Trimester Exam n/a Standard conversion grade scale 40% No

40

Practical Skills Assessment: Computer-based coding exam n/a Standard conversion grade scale 40% No

30

Assignment(Including Essay): Assignments n/a Standard conversion grade scale 40% No

25

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour