Identifying the Latent Space Geometry of Network Models through Analysis of Curvature / Shane Lubold, Arun G. Chandrasekhar, Tyler H. McCormick.

By:

Lubold, Shane

Contributor(s):

Material type: Text

TextSeries: Working Paper Series (National Bureau of Economic Research) ; no. w28273.Publication details: Cambridge, Mass. National Bureau of Economic Research 2020.Description: 1 online resource: illustrations (black and white)Subject(s):

Online resources:

Available additional physical forms:

Hardcopy version available to institutional subscribers

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.

Tags from this library: No tags from this library for this title. Log in to add tags.

Average rating: 0.0 (0 votes)

Holdings
Item type	Home library	Collection	Call number	Status	Date due	Barcode	Item holds
Working Paper	Biblioteca Digital	Colección NBER	nber w28273 (Browse shelf(Opens below))	Not For Loan

Total holds: 0

Collection: Colección NBER Close shelf browser (Hides shelf browser)

Previous	No cover image available	No cover image available	No cover image available	No cover image available	No cover image available	No cover image available	No cover image available	Next
Previous	nber w28270 Religion and Educational Mobility in Africa /	nber w28271 Gentrification and Neighborhood Change: Evidence from Yelp /	nber w28272 Dynamic Price Competition, Learning-By-Doing and Strategic Buyers /	nber w28273 Identifying the Latent Space Geometry of Network Models through Analysis of Curvature /	nber w28274 Specialization, Market Access and Real Income /	nber w28275 Effects of Reduced Workplace Presence on COVID-19 Deaths: An Instrumental-Variables Approach. /	nber w28276 Informal Central Bank Communication /	Next

December 2020.

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.