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Peter Diao : Model-Free Consistency of Graph Partitioning using Dense Graph Limits

The beautiful work of Borgs, Chayes, Lovasz, Sos, Szegedy, Vesztergombi, and many others on dense graph limits has received quite a bit of attention in pure math as well as statistics and machine learning. In this talk we will review some of the previous work on dense graph limits and then present recent work on providing a more robust mathematical framework for proving the statistical consistency of graph partitioning algorithms such as spectral clustering. A striking feature of our approach is that it is model-free, compared to the popular iid paradigm. Our results are thus broadly applicable in real-world settings, where it is notoriously difficult to obtain relevant models for network data, and observations are not independent. At the end, I will discuss implications for how mathematical foundations can be developed for other modern data analysis techniques. This is joint work with Dominique Guillot, Apoorva Khare, and Bala Rajaratnam. Preprint available at https://arxiv.org/abs/1608.03860.

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