DATA5441: Networks and High-dimensional Inference

General Information

2nd semester 2024, Lecturer: Eduardo G. Altmann.

Forum, Notebooks, etc.

We will use Edstem, accessible first time via Canvas.

Classes

Thursdays 9-11 and Fridays 9-11; Carslaw Building, 8th Floor, room 829 (AGR room).

Consultation time

Mondays 2pm-3pm, Carslaw 526.

Assessment

Exam (1/3), Assignments (1/3), and Project (1/3). Attendance is essential.

There will be in-class assignments every one or two weeks. The final assignment mark will be the mean of the individual assignment marks.

Project

The project takes place in Weeks 12 and 13.

Abstract

In our interconnected world, networks are an increasingly important representation of datasets and systems. This unit will investigate how this network approach to problems can be pursued through the combination of mathematical models and datasets. You will learn different mathematical models of networks and understand how these models explain non-intuitive phenomena, such as the small world phenomenon (short paths between nodes despite clustering), the friendship paradox (our friends typically have more friends than we have), and the sudden appearance of epidemic-like processes spreading through networks. You will learn computational techniques needed to infer information about the mathematical models from data and, finally, you will learn how to combine mathematical models, computational techniques, and real-world data to draw conclusions about problems. More generally, network data is a paradigm for high-dimensional interdependent data, the typical problem in data science. By doing this unit you will develop computational and mathematical skills of wide applicability in studies of networks, data science, complex systems, and statistical physics.

Objectives and learning outcome

Develop analytical, numerical, and modeling skills that help to connect abstract mathematical ideas to real-world systems represented as networks.

References

• Networks: An Introduction, Mark Newman, Oxford Univ Press, 2010.
• Network Science book, L. Barabasi, 2017 http://barabasi.com/networksciencebook/
• A First Course in Network Science, F. Menzer, S. Fortunato, and C. A. Davis, Cambrdige Univ. Press, 2020 [Online Version]
• Statistical mechanics of complex networks, R. Albert & A. Barabasi, Rev. Mod. Phys. 2002.
• The Structure and Function of Complex Networks, M. Newman, SIAM Review, 2002.

Computational resources

Networks:
• Networkx: https://networkx.github.io
• graphtool: https://graph-tool.skewed.de
• igraph: http://igraph.org
• Gephi: https://gephi.org/

Coding:
• Jupyter Notebooks: http://jupyter.org

Network data :

• Netzschleuder: https://networks.skewed.de/
• SNAP http://snap.stanford.edu/data/index.html
• SOPSAHL http://toreopsahl.com/datasets
• Index of Complex Networks – University of Colorado Boulder: https://icon.colorado.edu/

Tentative week-by-week outline

• 1 (1/8) Networks, data science, and high dimensions
• 2 (8/8) Centrality measures
• 3 (15/8) Random Graph Models
• 4 (22/8) Random Graphs vs. Complex Networks
• 5 (29/8) Mechanistic models: small world and preferential attachment
• 6 (5/9) Exponential Random Graph Models and Metropolis-Hastings method
• 7 (12/9) Stochastic Block Models and Statistical Inference
• 8 (19/9) Community Detection in Networks
• 9 (26/10) Network Resilience

(Mid-semester break)

• 10 (10/10) Cascades and spreading in Networks
• 11 (17/10) Games and discrete dynamics in Networks
• 12 (24/10) Continuous dynamical systems in Networks
• 13 (31/10) Project presentation and Exam preparation