DATA5441: Networks and High-dimensional Inference
1st semester 2020, Lecturer: Eduardo G. Altmann.
Forum, Notebooks, etc.
Online access (to classes and consultation)
Check information on the Edstem discussion page
Tuesdays 9-11 and Wednesdays 9-11, via Zoom (usual Meeting ID, see Ed).
Wednesdays 11am-12pm, via Zoom (Eduardo's Personal meeting ID 345 314 1592).
Exam (40%), Assignments (30%), and Project (30%). Attendance to class is essential.
There will be assignments every one or two weeks. The final assignment mark will be the mean of the individual assignment marks.
The project takes place in Weeks 12 and 13.
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.
- Networks: An Introduction, Mark Newman, Oxford Univ Press, 2010.
- Network Science book, L. Barabasi, 2017 http://barabasi.com/networksciencebook/
- Dynamical Processes on Complex Networks, A. Barrat, M. Barthélemy, A. Vespignani, Cambridge University Press, 2012
- 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.
Software for computation
- Networkx: https://networkx.github.io
- graphtool: https://graph-tool.skewed.de
- igraph: http://igraph.org
- Pajek: http://vlado.fmf.uni-lj.si/pub/networks/pajek/
- Jupyter Notebooks: http://jupyter.org
Network data :
- KONECT: http://konect.uni-koblenz.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 (24/2) Networks, data science, and high dimensions
- 2 (2/3) Centrality measures
- 3 (9/3) Random Graph Models
- 4 (16/3) Random Graphs vs. Complex Networks
- 5 (23/3) Mechanistic models: small world and preferential attachment
- 6 (30/3) Network Resilience
- 7 (6/4) Cascades and spreading in Networks
- 8 (20/4) Discrete dynamical systems in Networks
- 9 (27/4) Continuous dynamical systems in Networks
- 10 (4/5) Exponential Random Graph Models
- 11 (11/5) Community Detection in Networks
- 12 (18/5) Stochastic Block Models and inference
- 13 (25/5) Project presentation and Exam preparation