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Activity Number: 456 - Exploiting Lower-Dimensional Structure in Gaussian Process Regression
Type: Invited
Date/Time: Wednesday, August 10, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #320316
Title: A Gaussian Process Framework for Modeling with Network Inputs
Author(s): Nathaniel Josephs* and Lizhen Lin and Steven Rosenberg and Eric Kolaczyk
Companies: Yale University and The University of Notre Dame and Boston University and Boston University
Keywords: Gaussian process; multiple networks; graph classification; microbiome; preterm birth; Bayesian

While the study of a single network is well-established, technological advances now allow for the collection of multiple networks with relative ease. Increasingly, anywhere from several to thousands of networks can be created from brain imaging, gene co-expression data, or microbiome measurements. And these networks, in turn, are being looked to as potentially powerful features to be used in modeling. However, with networks being non-Euclidean in nature, how best to incorporate them into standard modeling tasks is not obvious. In this talk, we discuss a Gaussian process framework that provides a unified approach to binary classification, anomaly detection, and survival analysis with network inputs. We encode the networks in the kernel of a GP prior via their pairwise differences and show that our model achieves posterior consistency under several choices of graph distance that induce provably positive definite kernels. We provide an extensive simulation study to identify which distances perform the best for popular random graph models and to demonstrate that our model outperforms other state-of-the-art graph classifiers.

Authors who are presenting talks have a * after their name.

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