Permutation-Uniform Markov Chains on Networks

In this talk I introduce a generic, statistical model of longitudinal/panel network data analyzable with existing tools for popular, single-observation network models. The existing network models have been used since the 1980s to describe social networks of a fixed set of people whose friendships change over time, analogous to logistic regression where the regressors describe the network structure. The new model simplifies the analysis of some network and autoregressive models existing in the literature, and facilitates my introduction of a new network model.

The main modeling assumption is that the time series of network data is generated by a Markov chain whose parameterized transition probabilities have an ``exponential family'' form, which I will define in the talk. The key insight is that when every row of a Markov chain's transition matrix is a permutation of every other row, known as permutation uniformity, composing those permutations with the Markov chain itself produces an IID sequence of networks on the same nodes. This IID sequence can be viewed as a single observation of a multigraph whose probability distribution has an exponential family form with the same parameter as the transition probabilities. Statistical inference on the multigraph using existing ERGM (exponential random graph model) theory is valid for and interpretable in terms of the original network time series. In particular, the data storage requirements for the model are much smaller than for general models of Markov chains of networks.

Event Topic

Nonlinear Algebra and Statistics (NLASTATS)

Discrete Applied Math Seminar