# Spectral goodness-of-fit tests for complete and partial network data

@article{Lubold2021SpectralGT, title={Spectral goodness-of-fit tests for complete and partial network data}, author={Shane Lubold and Bolun Liu and T. McCormick}, journal={ArXiv}, year={2021}, volume={abs/2106.09702} }

Networks describe the, often complex, relationships between individual actors. In this work, we address the question of how to determine whether a parametric model, such as a stochastic block model or latent space model, fits a dataset well and will extrapolate to similar data. We use recent results in random matrix theory to derive a general goodnessof-fit test for dyadic data. We show that our method, when applied to a specific model of interest, provides an straightforward, computationally… Expand

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SHOWING 1-10 OF 53 REFERENCES

Universal Latent Space Model Fitting for Large Networks with Edge Covariates

- Computer Science
- J. Mach. Learn. Res.
- 2020

Two universal fitting algorithms for networks with edge covariates are presented: one based on nuclear norm penalization and the other based on projected gradient descent, motivated by maximizing the likelihood function for an existing class of inner-product models. Expand

Random Effects Models for Network Data

- 2003

One impediment to the statistical analysis of network data has been the difficulty in modeling the dependence among the observations. In the very simple case of binary (0-1) network data, some… Expand

Model Selection for Degree-corrected Block Models

- Computer Science, Medicine
- Journal of statistical mechanics
- 2014

The first principled and tractable approach to model selection between standard and degree-corrected block models is presented, based on new large-graph asymptotics for the distribution of log-likelihood ratios under the stochastic block model, finding substantial departures from classical results for sparse graphs. Expand

Spectral goodness of fit for network models

- Computer Science, Physics
- Soc. Networks
- 2015

SGOF provides an absolute measure of fit, analogous to the standard R-squared in linear regression, and is suitable for comparing network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. Expand

A Bootstrap Method for Goodness of Fit and Model Selection with a Single Observed Network

- Computer Science, Medicine
- Scientific Reports
- 2019

A subsampling bootstrap procedure is explored to serve as the basis for goodness of fit and model selection with a single observed network that circumvents the intractability of such likelihoods. Expand

Goodness of Fit of Social Network Models

- Mathematics
- 2008

We present a systematic examination of a real network data set using maximum likelihood estimation for exponential random graph models as well as new procedures to evaluate how well the models fit… Expand

Degree‐based goodness‐of‐fit tests for heterogeneous random graph models: Independent and exchangeable cases

- Mathematics
- Scandinavian Journal of Statistics
- 2019

The degrees are a classical and relevant way to study the topology of a network. They can be used to assess the goodness-of-fit for a given random graph model. In this paper we introduce… Expand

LATENT SPACE MODELS FOR MULTIVIEW NETWORK DATA.

- Computer Science, Medicine
- The annals of applied statistics
- 2017

This work departs from previous work in this area by representing dependence structure between network views through a multivariate Bernoulli likelihood, providing a representation of between-view association and infers correlations between views not explained by the latent space model. Expand

A goodness-of-fit test for stochastic block models

- Mathematics
- 2016

The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the… Expand

Latent Space Approaches to Social Network Analysis

- Mathematics
- 2002

Network models are widely used to represent relational information among interacting units. In studies of social networks, recent emphasis has been placed on random graph models where the nodes… Expand