A0859
Title: Kernel methods for estimating distributions of graph statistics
Authors: Jonathan Stewart - Florida State University (United States) [presenting]
Guang Qiu - Florida State University (United States)
Abstract: A novel framework is introduced for estimating distributions of discrete network statistics using kernel density estimation methods. While empirical distributions provide valuable insights into network structures, they often suffer from sample-specific artifacts and irregularities that obscure relevant features of the true underlying distribution. The methodology bridges an important methodological gap in network science by extending discrete kernel methods to network domains without imposing strong parametric assumptions, and can provide more accurate estimates of distributions of graph statistics. The methodology applies to a diverse range of network characteristics, including degree distributions, shared partner counts quantifying triadic closure in a network, geodesic distances, and more. Theoretical properties of the smoothed estimators are established, and principled methods are introduced for bandwidth parameter selection through cross-validation that account for inherent dependence among edges in the network. Through simulation studies across different network types and sizes, the approach is demonstrated to substantially reduce estimation error, as measured by total variation distance, when compared with the empirical distribution, providing more reliable inference on the true underlying distribution. Lastly, the methodology is demonstrated in a network data application.
