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Unit information: Anomaly Detection in 2018/19

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Unit name Anomaly Detection
Unit code MATHM0030
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 1B (weeks 7 - 12)
Unit director Dr. Patrick Rubin-Delanchy
Open unit status Not open

Probability 1, Statistics 1 and Statistics 2 (or equivalent)



School/department School of Mathematics
Faculty Faculty of Science


This unit aims to introduce models of normal network behaviour, anomaly detection, and the process of combining and screening anomalies over space and time.

It will provide the mathematical & statistical underpinnings of anomaly detection for cybersecurity data. It will cover the following topics: dynamic network models, fundamentals of hypothesis testing, combining and screening anomalies, Bayesian methods, Monte-Carlo approaches. In coursework assignments, students will use network, point process and cluster models to find anomalies in real cyber security data.

Intended learning outcomes

ILO1: to recognise and apply a range of models for dynamic network data, and their estimation

ILO2: to understand core anomaly detection concepts and tools, including mastering theory and interpretation of hypothesis tests, controlling false positive rates and performing meta-analysis

ILO3: to apply these anomaly detection tools to analyse real large-scale data and report the results

Teaching details

3 lectures per week for 6 weeks, to include 15 hours of new material and 3 hours of problem classes.

Assessment Details

Exam (80%) to assess ILOs 1 and 2.

Coursework assignment (20%) spanning the unit to assess ILO 3.

Reading and References

Casella, George, and Roger L. Berger. Statistical inference. Vol. 2. Pacific Grove, CA: Duxbury, 2002.

Daley, D. J., and D. Vere-Jones. An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods, Springer, New York, 2003.

Kolaczyk, E. D. Statistical analysis of network data: Methods and Models. Springer, New York, 2009.

Friedman, Jerome, Trevor Hastie, and Robert Tibshirani. The elements of statistical learning. (2nd edition), Springer, New York, 2009.

Heard, Nicholas A., et al. "Bayesian anomaly detection methods for social networks." The Annals of Applied Statistics 4.2 (2010): 645-662.