STAT Seminar: Identifying the Latent Space Geometry of Network Models Through Analysis of Curvature Event Logo

STAT Seminar: Identifying the Latent Space Geometry of Network Models Through Analysis of Curvature

by Information and Computer Sciences

Lecture Academics ICS Speaker Statistics

Thu, May 6, 2021

4 PM – 5 PM PDT (GMT-7)

Add to Calendar

Virtual

-

View Map
1
Registered

Registration

Details

The UCI Statistics Seminar Series is proud to present Tyler McCormick, Associate Professor of Statistics and Sociology, University of Washington.

Title: "Identifying the Latent Space Geometry of Network Models Through Analysis of Curvature"

Abstract: Statistically modeling networks, across numerous disciplines and contexts, is fundamentally challenging because of (often high-order) dependence between connections. A common approach assigns each person in the graph to a position on a low-dimensional manifold. Distance between individuals in this (latent) space is inversely proportional to the likelihood of forming a connection. The choice of the latent geometry (the manifold class, dimension, and curvature) has consequential impacts on the substantive conclusions of the model. More positive curvature in the manifold, for example, encourages more and tighter communities; negative curvature induces repulsion among nodes. Currently, however, the choice of the latent geometry is an a priori modeling assumption and there is limited guidance about how to make these choices in a data-driven way. In this work, we present a method to consistently estimate the manifold type, dimension, and curvature from an empirically relevant class of latent spaces: simply connected, complete Riemannian manifolds of constant curvature. Our core insight comes by representing the graph as a noisy distance matrix based on the ties between cliques. Leveraging results from statistical geometry, we develop hypothesis tests to determine whether the observed distances could plausibly be embedded isometrically in each of the candidate geometries. We explore the accuracy of our approach with simulations and then apply our approach to data-sets from economics and sociology as well as neuroscience.

Where

Virtual

-

Hosted By

Information and Computer Sciences | Website | View More Events

Contact the organizers