36-781, Advanced Statistical Network Models

Mini-semester II, Fall 2016

1:30--2:50 pm on Tuesdays and Thursdays in Wean Hall 5312
Office hours 11:00--12:00 on Tuesdays in Baker Hall 229C

Recent work on infinite-dimensional models of networks is based on the related notions of graph limits and of decomposing symmetric network models into mixtures of simpler ones. This course aims to bring students with a working knowledge of network modeling close to the research frontier. Students will be expected to complete projects which could be original research or literature reviews.


There are no formal pre-requisites, but the intended audience consists of students who are already familiar with networks, with statistical modeling, and with advanced probability. Others may find it possible to keep up, but you do so at your own risk.

Auditors are welcome, provided there is space for them in the classroom.


The class will cover the following topics, in roughly this order: exchangeable networks; the Aldous-Hoover representation theorem for exchangeable network models; limits of dense graph sequences ("graphons"); connection to stochastic block models; non-parametric estimation and comparison; approaches to sparse graphs. Additional topics or variations will depend on time and the interests of the class. See below for the precise list of lecture topics, subject to revision.


There is no required textbook for the class. The following are recommended, in roughly decreasing order of priority: In place of textbooks, students will be expected to read selected papers, as indicated below.

Course Mechanics

Class will meet twice a week. This will be a combination of lecture and seminar. Participation in class will be 50% of your grade; this will be equally divided between attendance (mandatory, except with permission of the professor) and scribing lecture notes, on a schedule to be determined.

There will be one assignment, the completion of a 15+ page report on material related to the course. This may be either original research or a literature review. All topics for reports must be approved by the professor by the half-way point in the course. An interim report will be due three weeks before the end of the semester, and a final report at the end of the semester. This report will be the other 50% of your grade.


Readings for the class will be linked in below. This is subject to revision.

25 October, Lecture 1: Conditionally-independent dyad processes
Lecture notes: PDF (correcting mis-statements from lecture), and Rnw source file
27 October, Lecture 2: Exchangeable networks and the Aldous-Hoover representation theorem
Scribed lecture notes by Momin Malik
1 November, Lecture 3: Limits of dense graph sequences
Scribed lecture notes by Nicolas Kim
3 November, Lecture 4: Graph limits and graphons
Lecture notes
8 November, Lecture 5: Laws of large numbers
Scribed notes by Alden Green
Instructor notes with details, complements, and exercises
10 November: NO LECTURE
10 November: deadline for proposing topics for your final report
15 November, Lecture 6: Graphons and standard network models; growing stochastic block models
17 November, Lecture 7: Nonparametric estimation of continuous latent space models
Scribed lecture notes by Abulhair Saparov
22 November, Lecture 8: Graph comparisons
Scribed lecture notes by Neil Spencer
29 November, Lecture 9: Nonparametric estimation of graphons
29 November: Interim reports due
1 December, Lecture 10: Nonparametric estimation of graphons, continued
Scribed lecture notes by Seth Cobb
6 December, Lecture 11: Nonparametric estimation of graphons, further continued
R for in-class demos
8 December, Lecture 12: Critique of exchangeability; approaches to sparse graph limits and sparse graphons
Scribed lecture notes by Cristobal De La Maza
14 December: Final reports due