Random graphical models

Causality in amongst confusion



Reading the The β€œIt’s really complicated and sad” theory of obesity put a question in my head about random structural models and what we can learn from them. I will be unlikely to return to and work through this right this minute, but it occurs to me that it is worth keeping around a list of models that sound like they are worth looking at

What is a good prior over causal graphs? With interactions? Good, in my current mode of thought, would mean, what classes of random causal graphs could e have that were intermediate in complexity between homogenous structure and maybe non-trivial structure. For example, monotonic, or multiplicative interactions with sparse links.

When we are concerned with sampling models over random graphs we might consider Exponential Random Graphs Model, a.k.a. ERGM models. I have some perfunctory notes on that theme under graph sampling. I wonder if that will subsume this idea or not?

I should read upon random graph theory and possible sparse random hypergraphs, e.g. Bapst and Coja-Oghlan (2016), as seen in theoretical analysis of message passing.

References

Amini, Hamed, Rama Cont, and Andreea Minca. 2013. β€œResilience to Contagion in Financial Networks.” Mathematical Finance, October, n/a–.
Bapst, Victor, and Amin Coja-Oghlan. 2016. β€œHarnessing the Bethe Free Energy.” Random Structures & Algorithms 49 (4): 694–741.
Du, Nan, Le Song, Ming Yuan, and Alex J. Smola. 2012. β€œLearning Networks of Heterogeneous Influence.” In Advances in Neural Information Processing Systems, 2780–88.
Gauthier, Daniel J., Erik Bollt, Aaron Griffith, and Wendson A. S. Barbosa. 2021. β€œNext Generation Reservoir Computing.” Nature Communications 12 (1): 5564.
Giryes, R., G. Sapiro, and A. M. Bronstein. 2016. β€œDeep Neural Networks with Random Gaussian Weights: A Universal Classification Strategy?” IEEE Transactions on Signal Processing 64 (13): 3444–57.
Glasserman, Paul, and H. Peyton Young. 2016. β€œContagion in Financial Networks.” Journal of Economic Literature 54 (3): 779–831.
Glymour, Clark. 2007. β€œWhen Is a Brain Like the Planet?” Philosophy of Science 74 (3): 330–46.
Goudarzi, Alireza, and Christof Teuscher. 2016. β€œReservoir Computing: Quo Vadis?” In Proceedings of the 3rd ACM International Conference on Nanoscale Computing and Communication, 13:1–6. NANOCOM’16. New York, NY, USA: ACM.
Grzyb, B. J., E. Chinellato, G. M. Wojcik, and W. A. Kaminski. 2009. β€œWhich Model to Use for the Liquid State Machine?” In 2009 International Joint Conference on Neural Networks, 1018–24.
Haldane, Andrew G, and Robert M May. 2011. β€œSystemic Risk in Banking Ecosystems.” Nature 469: 351–55.
Hirata, Hironori, and Robert E Ulanowicz. 1985. β€œInformation Theoretical Analysis of the Aggregation and Hierarchical Structure of Ecological Networks.” Journal of Theoretical Biology 116 (3): 321–41.
Martinsson, Per-Gunnar. 2016. β€œRandomized Methods for Matrix Computations and Analysis of High Dimensional Data.” arXiv:1607.01649 [Math], July.
Roca, Carlos P, Moez Draief, and Dirk Helbing. 2011. β€œPercolate or Die: Multi-Percolation Decides the Struggle Between Competing Innovations.”
Scardapane, Simone, and Dianhui Wang. 2017. β€œRandomness in Neural Networks: An Overview.” Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 7 (2).
Stadler, Peter F, Walter Fontana, and John H Miller. 1993. β€œRandom Catalytic Reaction Networks.” Physica D: Nonlinear Phenomena 63 (3-4): 378–92.
Watts, Duncan J., and Peter Sheridan Dodds. 2007. β€œInfluentials, Networks, and Public Opinion Formation.” Journal of Consumer Research 34 (4): 441–58.
Wigner, Eugene P. 1955. β€œCharacteristic Vectors of Bordered Matrices With Infinite Dimensions.” The Annals of Mathematics 62 (3): 548.

No comments yet. Why not leave one?

GitHub-flavored Markdown & a sane subset of HTML is supported.