Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

 
Session Overview
Session
MS196: Algebro-geometric methods for social network modelling
Time:
Saturday, 13/Jul/2019:
10:00am - 12:00pm

Location: Unitobler, F-121
52 seats, 100m^2

Presentations
10:00am - 12:00pm

Algebro-geometric methods for social network modelling

Chair(s): Kayvan Sadeghi (University College London, United Kingdom)

Algebraic and geometric methods have recently been proposed for statical random (social) network models. These methods could be described in three categories:

1) Understanding the geometry of the network models, especially the exponential random graph models (ERGMs) in order to understand the (mis)behaviour of such models in the asymptotic settings, commonly known as degeneracy of such models, which occurs commonly. In addition, many ERGMs are in fact curved exponential families, and understanding the geometry of the parameter space is of great importance.

2) Finding the model polytope of network models, i.e. the polytope of all sufficient statistics for every network of fixed size n in order to determine the existence of the MLE for such models and also to demonstrate which parameters are actually estimable.

3) Understanding the Markov bases of random network models specified by a multi-homogeneous ideal. This is directly relevant to the goodness-of-fit testing problems for network models as well as simulating from these models.
In this minisymposium some of the experts of the field of random network analysis demonstrate the latest developments on the algebro-geometric methods as described above.

The minisymposium would consist of four speakers, some of whom have already agreed to reset their papers. A tentative list is as follows (I will ad them to the list when the attendance is finalized by the authors):

 

(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)

 

Goodness-of-fit testing for log-linear network models

Despina Stasi
Illinois Institute of Technology

We define and study degree and block-based ERGMs called log-linear ERGMs. These models admit a correspondence to contingency table models which gives us access to categorical data analysis tools. We use these tools in combination with sampling tools stemming from discrete mathematics and algebraic statistics to produce a non-asymptotic goodness-of-fit test of network data to these models.

 

Cores, shell indices and the degeneracy of a graph limit

Johannes Rauh
Max-Plack Institute

The k-core of a graph is the maximal subgraph in which every node has degree at least k, the shell index of a node is the largest k such that the k-core contains the node, and the degeneracy of a graph is the largest shell index of any node. After a suitable normalization, these three concepts generalize to limits of dense graphs (also called graphons). In particular, the degeneracy is continuous with respect to the cut metric.

 

On Exchangeability in Network Models

Kayvan Sadeghi
University College London, United Kingdom

We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their implications, between statistical network models that are finitely exchangeable and models that define a consistent sequence of probability distributions on graphs of increasing size. We also show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts. We then characterize all possible conditional independence structures for finitely exchangeable random graphs.