NETS 7976 - Network Reconstruction and Inference from Dynamics - Spring 2024

Wednesdays: 10:00 – 11:30am
January 10 – April 24, 2024
177 Huntington, room 207

Summary

This class is an introduction to network reconstruction techniques using time series data. Using time series data derived from underlying network dynamics to reconstruct said networks is an open field of study combining network science, time series analysis, and statistics. The course will focus on the mathematical foundation behind multivariate time series analysis, information theory, and network dynamics and how each interplay to reconstruct networks. This course is especially relevant as networks are frequently presented using time series data, e.g., neuron's firing, stock price fluctuations, climate changes, etc., where each node has a time series which is affected by it's neighbors based on underlying network dynamics. Hence, there is an increasing need to understand how to use these time series to reconstruct the true network. Students will leave the class with an understanding of the tools used in multivariate time series analysis and have experience using these tools to reconstruct networks. This class is designed in collaboration with Cory Glover, a third-year PhD student in Network Science.

Coursework, Class Structure, Grading

The course adopts a flipped classroom concept: Students are exposed to the relevant material through pre-recorded video lectures, readings, and exercises that involve both analytic calculation and coding. The in-class hours are dedicated to recapitulation of the most important points, clarification of questions, as well as open discussion. The grading of the course is based on active participation in discussions and continual work on exercises. In a typical class students will summarize the main points of the lectures in their own words. The weekly exercises and questions, that students prepare prior to class, structure the in class discussion. Discussions will remain open and allow to explore topics deeper as needed.

Learning Objectives and Outcomes

By the end of this course students should have a deep familiarity with common used techniques of multivariate time series analysis and how to apply them to network reconstruction. In particular, they will develop an understanding of the strengths and pitfalls, similarities and dissimilarities of common multivariate analysis methods. They will learn how information theory and Bayesian statistics combine with these methods in order to reconstruct networks. Lastly, they will combine this knowledge with data to practice implementation of these approaches and explore how network topology and network dynamics influence the reconstruction of said networks. Students should leave the course able to reconstruct networks using multivariate time series data and have an understanding of the strengths and pitfalls of the methods chosen. This course will achieve these objectives while being:

• Current: Through the discussion of research papers and textbook chapters in the course, students should learn to identify concepts from multivariate time series analysis, information theory, and network science and recognize how they can be combined in order to reconstruct networks.

• Practical: The course will include implementing the methods learned and analyzing their performance when used for network reconstruction. It will also has mathematical exercises where applicable from the course reading in order to understand the derivation of said techniques.

• Actionable: The open structure of in-class discussion encourages students to explore the application of the course material to their own area of research as well as exploring open questions within the topic of network reconstruction.

Evaluation

The course evaluation is based on two components:

1. Active participation in the weekly meetings: This includes active participation in discussions through posing relevant questions, engaging in discussion around the assigned readings and presenting solved problems, relevant code and any additional exploratory research.

2. Completion and presentation of a final project: The project gives students a chance to show their ability to reconstruct networks from multivariate time series and exhibit deep understanding of the methods used. It can take the form of a research paper, literature review, etc. The presentation of the results in the final week of the semester is part of the evaluation.

Materials

This course will primarily use current, published research papers as the readings for the course. These papers are categorized into (i) multivariate time-series analysis papers and (ii) network reconstruction papers. For the study of multivariate time-series analysis, we will use Unifying pairwise interactions in complex dynamics as a basis of study as it provides a framework unifying many techniques commonly used. For the topic of network reconstruction, we will learn reconstruction methods from both information theoretical and Bayesian statistic approaches. The informational theoretical readings will come from An Introduction to Transfer Entropy (2016) by Bossomaier et al. as well as other related papers. The Bayesian statistic approach will be taught from Tiago Peixoto's 2019 paper Network Reconstruction and Community Detection from Dynamics.

Instructor

Brennan Klein is an associate research scientist at the Network Science Institute, with a joint affiliation at the Institute for Experiential AI. He is the director of the Complexity & Society Lab. His research spans two broad topics: 1) Information, emergence, and inference in complex systems — developing tools and theory for characterizing dynamics, structure, and scale in networks, and 2) Public health and public safety — creating and analyzing large scale datasets that reveal inequalities in the United States, from epidemics to mass incarceration. Dr. Klein received a PhD in Network Science in 2020 from Northeastern University and got his BA in Cognitive Science & Psychology from Swarthmore College in 2014. Website: http://brennanklein.com.

Syllabus below (or pdf here).

Week 2: Jan. 17

Basic/Distance/Casual Time Series Analysis Methods

Readings:

• Primary reading: Cliff, Oliver M., et al. Unifying pairwise interactions in complex dynamics. Nature Computational Science 3.10 (2023): 883-893. Supp. 1.1-1.3.

• Primary reading: Associated references for methods defined in Supplement above.

  • Supplementary reading: Cliff, O. M. DynamicsAndNeuralSystems/pyspi (Zenodo, 2023); https://doi.org/10.5281/zenodo.8223340.

Week 3: Jan. 24

Spectral and Miscellaneous Approaches

Readings:

• Primary reading: Cliff, Oliver M., et al. Unifying pairwise interactions in complex dynamics. Nature Computational Science 3.10 (2023): 883-893. Supp. 1.5-1.6.

• Primary reading: Associated references for methods defined in Supplement above.

  • Supplementary reading: Cliff, O. M. DynamicsAndNeuralSystems/pyspi (Zenodo, 2023); https://doi.org/10.5281/zenodo.8223340.

  • Supplementary reading: Haas, M., Goswami, B., & von Luxburg, U. (2023). Pitfalls of Climate Network Construction—A Statistical Perspective. Journal of Climate, 36(10), 3321-3342.

Week 4: Jan. 31

Information Theoretic Approaches

Readings:

• Primary reading: Cliff, Oliver M., et al. Unifying pairwise interactions in complex dynamics. Nature Computational Science 3.10 (2023): 883-893. Supp. 1.4.

• Primary reading: Associated references for methods defined in Supplement above.

• Primary reading: An Introduction to Transfer Entropy. Chap. 4.1-4.2.

  • Supplementary reading: https://www.youtube.com/@JosephLizier

  • Supplementary reading: Donges, J. F., Zou, Y., Marwan, N., & Kurths, J. (2009). The backbone of the climate network. Europhysics Letters, 87(4), 48007.