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Mixed Effects Model on Functional Manifolds / Sampling Directed Networks

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STSW02 - Statistics of geometric features and new data types

I would like to talk about two projects. Co-authors of Mixed Effects Model on Functional Manifolds: John Aston (University of Cambridge), Lexin Li (UC Berkeley) We propose a generalized mixed effects model to study effects of subject-specific covariates on geometric and functional features of the subjects' surfaces. Here the covariates include both time-invariant covariates which affect both the geometric and functional features, and time-varying covariates which result in longitudinal changes in the functional textures. In addition, we extend the usual mixed effects model to model the covariance between a subject's geometric deformation and functional textures on the surface. Co-authors of Sampling Directed Networks: Richard Davis (Columbia University), Gennady Samorodnitsky (Cornell University), Zhi-Li Zhang (University of Minnesota). We propose a sampling procedure for the nodes in a network with the goal of estimating uncommon population features of the entire network. Such features might include tail behavior of the in-degree and out-degree distributions and as well as their joint distribution. Our procedure is based on selecting random initial nodes and then following the path of linked nodes in a structured fashion. In this procedure, targeted nodes with desired features, such as large in-degree, will have a larger probability of being retained. In order to construct nearly unbiased estimates of the quantities of interest, weights associated with the sampled nodes must be calculated. We will illustrate this procedure and compare it with a sampling scheme based on multiple random walks on several data sets including webpage network data and Google+ social network data.

This talk is part of the Isaac Newton Institute Seminar Series series.

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