Network Model Theory
Contents
11. Network Model Theory#
In this section, we’ll do a much deeper dive into the intricacies of network modelling. It is important to note that the models you’ll learn about here may sound a little different from the models you saw earlier in the book, but this in intentional: in this section we’ll be describing the models using far more statistically precise language. With this added language in hand, which may appear cumbersome at first, you can describe a wide variety of variations of the models you learned about previously. You’ll be able to more succinctly, and more directly, understand exactly what is being modelled, what is being treated as random, and what is being treated as fixed. Many of the strategies that you learned about in previous sections, such as the latent position testing and latent distribution testing in Section 7.1 become a lot more digestable when you understand them as tests which assume slightly different statistical models. Let’s get to it. In this section, you’ll learn the following aspects:
Background gives an introduction to the mathematical and probability concepts to be aware of before reading the remainder of the section.
Foundation gives the probabilistic foundations and motivations for graph models.
11.1. References#
Throughout this section, we make use of results from a variety of papers, which are largely captured by [3] and [4].
- 1
Avanti Athreya, Donniell E. Fishkind, Minh Tang, Carey E. Priebe, Youngser Park, Joshua T. Vogelstein, Keith Levin, Vince Lyzinski, and Yichen Qin. Statistical inference on random dot product graphs: a survey. J. Mach. Learn. Res., 18(1):8393–8484, January 2017. doi:10.5555/3122009.3242083.
- 2
Jaewon Chung, Eric Bridgeford, Jesús Arroyo, Benjamin D. Pedigo, Ali Saad-Eldin, Vivek Gopalakrishnan, Liang Xiang, Carey E. Priebe, and Joshua T. Vogelstein. Statistical Connectomics. Annu. Rev. Stat. Appl., 8(1):463–492, March 2021. doi:10.1146/annurev-statistics-042720-023234.