Objectives:
To engage students in statistical learning and algorithmic analysis of multilayer network models, which constitute a modern development in data science for integrating diverse types of data emerging from the same complex system such as a biological, transportation or climate system.
Course Contents:
Course to be organised as a coherent blend of student-led and instructor-led sessions around themes that provide necessary background and discuss active research related to statistical reconstruction/learning of multi-layer networks from data, algorithmic analysis of the emergent structural/dynamical properties of such networks, and intra- vs. inter-layer network contributions to system behavior.
- THEME 0: Motivation and Background - Various application domains motivating multilayer networks; Definition of a multilayer network
(in simple terms, a collection of multiple graphs describing a complex system, with one graph per layer encoding distinct relationships
over the same set of objects and optional links connecting across layers; also called multi-relational or multiplex or interconnected
networks, not to be confused with perceptrons in deep learning); Background on unilayer networks (traditional graphical model learning
and graph algorithms).
- THEME 1: Multilayer network learning - Structure learning and parameter estimation of select graphical models: multi-layered GGMs
(Gaussian Graphical Models) that share information across layers, or have directed links (chains) between layers, etc.
- THEME 2: Multilayer network analysis - Algorithms for spectral clustering of multilayer networks; Algorithms to calculate betweenness
centrality, overrepresented subnetwork motif counts and other graph-theoretic measures capturing emergent structural properties of
multilayer networks; Information flows or other dynamical processes on multilayer networks, especially with coupling across layers.
- THEME 3: Multilayer network applications - Introduction to the two application domains focused in this course (multi-tissue biological
system and multi-view climate system); Research work of primarily applied nature where methods developed in above themes are
applied to networks such as a complex biological or climate system.
Learning outcomes:
Through the course, students learn to think critically about the theoretical and applied aspects of statistical learning and combinatorial graph algorithms related to multilayer or multiplex networks, and thereby acquire skills to transform multi-modal data describing a complex system into key insights about system behavior.
Text Books:
- Mikko Kivelä, Alex Arenas, Marc Barthelemy, James Gleeson, Yamir Moreno, and Mason A. Porter (2014). Multilayer networks.
Journal of Complex Networks, 2(3):203-271.
- Trevor Hastie, Robert Tibshirani, and Jerome Friedman (2009). The Elements of Statistical Learning: Data Mining, Inference, and
Prediction, Second Edition (Chapter 17 on Graphical Models). Springer, ISBN: 0387848576.
- Thomas Cormen, Charles Leiserson, Ronald Rivest, and Clifford Stein (2009). Introduction to Algorithms, 3rd Edition (Chapters in
Part VI on Graph Algorithms). The MIT Press, ISBN: 0262033844.
Reference Books:
- S. Boccaletti, G. Bianconi, R. Criado, C. I. del Genio, J. Gómez-Gardenes, M. Romance, I. Sendina-Nadal, Z. Wang, and M. Zanin
(2014). The structure and dynamics of multilayer networks. Physics Reports, 544(1):1-122.
- Avrim Blum, John Hopcroft, and Ravindran Kannan (2017). Foundations of Data Science (Chapter 7 on (Spectral) Clustering). To be
published.
- Various research papers on theoretical and applied aspects of multilayer networks.
