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NUMERICAL OPTIMISATION
PROJECT GUIDELINES
Optimisation in classification with Support Vector Machines (SVMs)
Submit a single PDF report via Moodle by 4pm (UK time) on Wednesday 23rd of April 2025.
To facilitate marking, please include the optimisation method in the name of the submitted PDF file and in the header/title of your report.
Scope:
This is a numerical optimisation and not a machine learning project. The emphasis here is on optimisation methods and their convergence not on classification performance. The task is to take an application problem, translate it into mathematical optimisation formulation abstract from the application, then solve and analyse it as an optimisation problem.
Report:
To achieve full marks (as in brackets [n pt]) the report needs to be well structured (address each point completely in a dedicated section), be written clearly and logically while succinct, mathematically rigorous (on par with the lecture), use consistent notation, and be self contained i.e. include everything the reader needs to understand it. This does not mean you should include proofs of theorems, find a way to make a coherent argument without including the proofs.
Always provide references to sources of any claims, theorems, methods etc (avoid Wikipedia, good Wiki contributions state original sources!).
Do not expect us to search in your text for arguments, guess what you may have meant,look things up, or accept any statements without coherent supporting argument with reference to sources.
3k words is a total hard limit (code excluded), please include the word count.
Code:
Include your implementation of the optimisation method and an excerpt from your testing script showing how it is called (keep it to minimum necessary to validate that you used your own implementation, use highlighting if necessary), as two separate and clearly labelled appendices in your report.
Collate report and code as one single PDF document for submission. The code will not count towards the word limit. You will only get full points for parts II & III if code is included.
UCL rules and regulations on late submission and plagiarism apply. Use of chatGPT and similar is not allowed.
Support vector machines (SVMs) are a well established and rigorously founded techniquefor solution of classification problems in machine learning.
Optimisation method and convergence theory in the context of your problem:
You may want to introduce a method which was not on the syllabus and apply it to your optimisation problem. The bonus points awarded will depend on the level of difficulty of the chosen method and the theory involved.
(d) Discuss theoretical convergence rates predicted for your problem. For more details see below (†).[5 pt]
(†) To argue convergence in (c,d) paraphrase theorems from the lecture or other respectable sources (books, journals, trusted lecture notes etc). Always state the complete result, this may involve combining multiple lemmas and theorems into a coherent theorem (reference all sources, unify notation!). Explain why this result applies to your problem i.e. check the assumptions against the properties of your problem. If you cannot exactly match the problem with the theory explain this clearly and discuss what is the departure from the theory in your case and what effect on convergence do you expect and why.
Marks: 25 pt baseline + up to 25 pt bonus (method substantially different to those on the syllabus, different convergence theorems, etc). [: 25 - 50 pt]
Note: Without a serious attempt on numerical solution, the project will not achieve a pass
(b) Provide one relevant convergence plot and discuss the empirical convergence rate qualita tively (e.g. linear/quadratic/superlinear, etc; no need to calculate the precise rate). [5 pt]
(d) Discuss the theoretical versus empirical performance of the method in terms of complexity, CPU time, memory used. [5 pt]