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MA3K1 Mathematics of Machine Learning

Lecturer: Martin Lotz

Term(s): 1

Status for Mathematics students:

Commitment: 10 x 3 hour lectures, support classes.

Assessment: Two hour exam 85% and Assignments 15%

Prerequisites: MA260 Norms Metrics and Topologies, MA228 Numerical Analysis or MA261 Differential Equations: Modelling and Numerics.

Leads To:

Content:

Fundamentals of statistical learning theory

- Regression and classification

- Empirical risk minimization and regulation

- VC theory

Optimization

- Basic algorithms (gradient descent, Newton’s method)

- Convexity, Lagrange duality and KKT theory

- Quadratic optimization and support vector machines

- Subgradients and nonsmooth analysis

- Proximal gradient methods

- Accelerated and stochastic algorithms

Machine learning

- Neural networks and deep learning

- Stochastic gradient descent

- Kernel methods and Gaussian processes

- Recurrent neural networks

- Applications (pattern recognition, time series prediction)

      - Applications (pattern recognition, time series prediction)

      Aims:

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

      Objectives:

      By the end of the module the student should be able to:

      - Describe the problem of supervised learning from the point of view of function approximation, optimization, and statistics.

      - Identify the most suitable optimization and modelling approach for a given machine learning problem.

      - Analyse the performance of various optimization algirthms from the point of view of computational complexity (both space and time) and statistical accuracy.

      - Implement a simple neural network architecture and apply it to a pattern recognition task.

      Books:

      1. Friedman, Jerome, Trevor Hastie, and Robert Tibshirani. The elements of statistical learning. Springer series in statistics, 2001.
      2. Beck, Amir. First-Order Methods in Optimization. Vol. 25. SIAM, 2017.
      3. Vapnik, Vladimir. The nature of statistical learning theory. Springer, 2013.
      4. Cucker, Felipe, and Ding Xuan Zhou. Learning theory: an approximation theory viewpoint. Vol. 24. Cambridge University Press, 2007.

      5. Higham, Catherine F., and Desmond J. Higham. "Deep Learning: An Introduction for Applied Mathematicians." arXiv preprint arXiv:1801.05894 (2018).

      Additional Resources

      yr1.jpg
      Year 1 regs and modules
      G100 G103 GL11 G1NC

      yr2.jpg
      Year 2 regs and modules
      G100 G103 GL11 G1NC

      yr3.jpg
      Year 3 regs and modules
      G100 G103

      yr4.jpg
      Year 4 regs and modules
      G103

      Archived Material
      Past Exams
      Core module averages