[ugrads] Seminar Talk on Tuesday, 12:45pm, RE 102

Hemanshu Kaul kaul at iit.edu
Mon Jan 14 11:23:11 CST 2019

Hello all,

Welcome to the new year and a new semester!

We have the first Discrete Math seminar talk of the semester (jointly with
Algebraic Statisitics seminar) *tomorrow, Tuesday, 1/15, at 12:45pm-1:45pm,
in RE 102.* *Billy Schwartz* will speak on his work related to statistical
models for dynamic (time-evolving)  networks. Billy will make the talk
accessible to all with `` passing familiarity with basic probability,
linear algebra, and graph theory''. The talk will include ``a primer on
exponential families, Markov chains, and random networks''.

The details of the talk are given below.

I hope to see you there.


*Title: Permutation-uniform Markov chains on networks *

* William Schwatrz, IIT*

*Date:** Tuesday, 1/15, 12:45pm-1:45pm *

*Place**: RE 102*

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.


Hemanshu Kaul
Associate Professor of Applied Mathematics
Co-Director, Graduate Program on Decision Sciences (CDSOR)
Illinois Institute of Technology
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