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This is a joint exit seminar for Robert Bassett and Kirill Paramanov. Rob's talk will be from 12:10 to 12:35, while Kirill's talk will be from 12:40-13:05

Abstract for Robert's talk: We introduce a new method for nonparametric density estimation on geometric networks. By penalizing a maximum likelihood approach with a total variation penalty, we avoid overfitting and the dirac curse. We provide results which reduce the search space for the estimator from infinite dimensional function space to the finite-dimensional setting, and further demonstrate its computational tractability. We then focus on the asymptotic convergence rate of this density estimation method. Lastly, we review applications to the defense of infrastructure networks.

Abstract for Kirill's talk: Extracting data from social networks becomes more and more important because of the wide applicability of such algorithms. For the large graphs (like Facebook), where the access to the whole graph is not feasible, the best option is to have an on-line learning procedure while travelling from vertex to vertex, and gather information about the local structure of the graph.

An important local statistic of a network is graphlet count- the number of occurrences of a small motif (e.g. a wedge or a triangle) in the big network. In this talk I propose a new Lifting algorithm to construct an estimate for the graphlet count statistic, which has an advantage of having low correlation between samples and being universal for all types of graphlets.
I also propose several modifications for the algorithm, each one applicable to a specific goal, making the estimator versatile for different problems.

Robert's Website: http://mathfactsoflife.com/

Kirill's Website: https://www.math.ucdavis.edu/~kirill/

There will be Chickpeas! Register here.