An Annotated Graph Model with Differential Degree Heterogeneity for Directed Networks
Authors: Stefan Stein, Chenlei Leng; Journal of Machine Learning Research, 24(119):1−69, 2023.
Abstract
Graphs are commonly used to represent directed networks, where the ordered edges represent interactions between vertices. However, there is a lack of statistical models suitable for inference, especially when considering contextual information and degree heterogeneity. This paper introduces an annotated graph model that explicitly incorporates parameters to account for these features. To address the issue of modeling degree heterogeneity, a sparsity assumption is proposed, and a penalized likelihood approach with L1-regularization is used for parameter estimation. The consistency of this approach in estimation and selection is studied under the assumption of a sparse network, and it is shown that inference on the covariate parameter is straightforward, eliminating the need for debiasing commonly used in L1-penalized likelihood estimation. Theoretical findings are supported by simulation and data analysis.
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