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> Mathematical Programming and Research Methods
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Mathematical Programming and Research Methods
Note:
Whilst every effort is made to keep the syllabus and assessment records correct
for this course, the precise details must be checked with the lecturer(s).
| Code: | GI07
(Also taught as: M012)
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| Year: | MSc |
| Prerequisites: | Part A: Proficiency in at least one high-level programming language such as C, C++, Pascal or Java etc as the course does not teach programming skills from scratch. Prior programming expertise is needed so that the new languages can be introduced quickly. Part B: although this course is not mathematically rigorous students should be at home in multivariate calculus and linear algebra. |
| Term: | 1 (Programming Issues) and 2 [Experimental Design) |
| Taught By: | Mark Herbster (Part A) (50%)
TBC (Part B) (50%)
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| Aims: | The aims of the Programming Issues part of this course are: to provide a practical knowledge and understanding of the programming environments of Matlab and Mathematica. Knowledge of and proficiency in these languages/packages form an essential component of courses GI06 (Evolutionary Systems) and GI01 (Supervised Learning). The aim of the Experimental Design and Analysis part of the course is to prepare students for effective project work using appropriate techniques for computer science research projects. |
| Learning Outcomes: | Part 1 - Programming Issues: To be able to program in Matlab and Mathematica and to recognize their strengths and weaknesses versus conventional programming languages. Part 2 - Experiemental Design and Analysis: To be able to apply appropriate techniques for computer science research projects. |
Content:
| Part A - Programming Issues | |
| Matlab | Matrix Operations
Control flow
I/O
Script files
2d and 3d graphics |
| Mathematica | Symbolic mathematics
List processing
Control flow
Functions
Graphics |
| Part B - Experimental design and analysis | |
| Motivation | Normative scientific methods - What are experiments?
Making inferences from data
Agreed rules of good scientific practice
What really happens (Kuhnian theory)
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| Probability and Distribution Theory | The role of probability in scientific research
Probability axioms - interpretation of probability (subjective and / or
frequency based)
The major probability distributions
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| First Steps in Inference | Bayes Theorem for discrete and continuous cases
Alternative ideas about statistical inference - sampling based approaches vs
Bayes theorem approaches
Practical resolution of this controversy |
| Estimation Theory | Concept of an estimator - sampling distributions - bias, consistency,
sufficiency
Confidence intervals |
| Statistical Testing | Statistical hypothesis testing principles and practice
Bayesian approach
Type I and II errors
The range of the usual basic statistical tests |
| Factorial Experimental Design | Motivation, examples, case studies
Simple 1 way, 2 way ANOVA and the concept of non-additivity - interaction |
| Relationship | Simple linear regression and correlation |
| The General Linear Model | Introduction of the model
Demonstration of its generality
Estimation of the parameters, confidence intervals, tests of goodness of
fit of the models |
| Generalised Linear Iterative Models (GLIM) | The exponential family of distributions
Poisson log-linear models, logistic regression |
| Questionnaire Design | Good practice in designing and validating a questionnaire
Problems about ordinal, interval and ratio scales, and using non-interval
variables as if they were interval
Motivation for non-parametric statistics - introduce basic ideas |
| Principal Components Analysis | Data reduction
Factor analysis methods
Applications |
Method of Instruction:
Part A: Lecture presentations with intensive programming coursework which is oriented towards machine learning. Part B: Lecture presentations with associated class problems. Part A and Part B are equally weighted. Full details of coursework to be set will be provided by the lecturers for this course.
Assessment:
The course has the following assessment components:
- Coursework Section (1 piece, 100 %)
To pass this course, students must:
Resources:
Mastering MATLAB 6: A Comprehensive Tutorial and Reference by Duane Hanselman and Bruce R. Littlefield, Prentice Hall,
The Mathematica Book, Stephen Wolfram, Cambridge University Press, ISBN 0-521-64314-7.
The Definitive Guide to Project Management, Sebastian Nokes et al, Financial Times Prentice Hall, 2003
ISBN 0 273 66397 6
The Mythical Man-Month, Fredrick P Brooks, Addison-Wesley, 1995 Anniversary edition, Addison -Wesley
ISBN 0 201 83595 9
Leading Change, John P. Kotter, Harvard business School Press, 1996
ISBN 0 87584 747 1
Agile Software Development Ecosystems, Jim Highsmith, Addison-Wesley, 2002
ISBN 0 201 76043 6
In addition during the course you will be provided with both printed copies and references for research articles.
Lecture notes
General Information on Matlab and Mathematica
MSc Intelligent Systems Homepage
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