Distance Shrinkage and Euclidean Embedding via Regularized Kernel Estimation

Zhang, Luwan; Wahba, Grace; Yuan, Ming

doi:10.48550/arxiv.1409.5009

Cited by 1 publication

(1 citation statement)

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“…]. This would be easily solved (if a solution exists) using the tools of multidimensional scaling [7] if not for the condition that each α(i, •) must be nonnegative and sum to m. We are exploring possible approximation approaches for this problem, including alternately projecting onto the cone of distance matrices [58] and the polytope defining the constraints on the α's. An approximate solution for this is essential, as it would allow us to use the generalized omnibus framework to induce a given correlation structure in embedded space.…”

Section: Discussionmentioning

confidence: 99%

The Importance of Being Correlated: Implications of Dependence in Joint Spectral Inference across Multiple Networks

Pantazis,

Athreya,

Arroyo

et al. 2020

Preprint

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Spectral inference on multiple networks is a rapidly-developing subfield of graph statistics. Recent work has demonstrated that joint, or simultaneous, spectral embedding of multiple independent network realizations can deliver more accurate estimation than individual spectral decompositions of those same networks. Little attention has been paid, however, to the network correlation that such joint embedding procedures necessarily induce. In this paper, we present a detailed analysis of induced correlation in a generalized omnibus embedding for multiple networks. We show that our embedding procedure is flexible and robust, and, moreover, we prove a central limit theorem for this embedding and explicitly compute the limiting covariance. We examine how this covariance can impact inference in a network time series, and we construct an appropriately calibrated omnibus embedding that can detect changes in real biological networks that previous embedding procedures could not discern. Our analysis confirms that the effect of induced correlation can be both subtle and transformative, with import in theory and practice.

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Section: Discussionmentioning

confidence: 99%