Course Announcements: Statistical Network Models, Fall 2016

Attention conservation notice: Self-promotion, and irrelevant unless you (1) will be a student at Carnegie Mellon in the fall, or (2) have a morbid curiosity about a field in which the realities of social life are first caricatured into an impoverished formalism of dots and lines, devoid even of visual interest and incapable of distinguishing the real process of making movies from a mere sketch of the nervous system of a worm, and then further and further abstracted into more and more recondite stochastic models, all expounded by someone who has never himself taken a class in either social science or any of the relevant mathematics.

Two, new, half-semester courses for the fall:

36-720, Statistical Network Models

6 units, mini-semester 1; Mondays and Wednesdays 3:00--4:20 pm, Baker Hall 235A

This course is a rapid introduction to the statistical modeling of social, biological and technological networks. Emphasis will be on statistical methodology and subject-matter-agnostic models, rather than on the specifics of different application areas. There are no formal pre-requisites, and no prior experience with networks is expected, but familiarity with statistical modeling is essential.

Topics (subject to revision): basic graph theory; data collection and sampling; random graphs; block models and community discovery; latent space models; "small world" and preferential attachment models; exponential-family random graph models; visualization; model validation; dynamic processes on networks.

36-781, Advanced Network Modeling

6 units, mini-semester 2; Tuesdays and Thursdays 1:30--2:50 pm, Wean Hall 5312

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.

Topics (subject to revision): 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.

720 is targeted at first-year graduate students in statistics and related fields, but is open to everyone, even well-prepared undergrads. Those more familiar with social networks who want to learn about modeling are also welcome, but should probably check with me first. 781 is deliberately going to demand rather more mathematical maturity. Auditors are welcome in both classes.

Corrupting the Young; Networks; Enigmas of Chance