Stochastic Step-wise Feature Selection for Exponential Random Graph Models (ERGMs)

Statistical analysis of social networks provides valuable insights into complex network interactions across various scientific disciplines. However, accurate modeling of networks remains challenging due to the heavy computational burden and the need to account for observed network dependencies. Exponential Random Graph Models (ERGMs) have emerged as a promising technique used in social network modeling to capture network dependencies by incorporating endogenous variables. Nevertheless, using ERGMs poses multiple challenges, including the occurrence of ERGM degeneracy, which generates unrealistic and meaningless network structures. To address these challenges and enhance the modeling of collaboration networks, we propose and test a novel approach that focuses on endogenous variable selection within ERGMs. Our method aims to overcome the computational burden and improve the accommodation of observed network dependencies, thereby facilitating more accurate and meaningful interpretations of network phenomena in various scientific fields. We conduct empirical testing and rigorous analysis to contribute to the advancement of statistical techniques and offer practical insights for network analysis.

Discussion of Multiscale Fisher's Independence Test for Multivariate Dependence

The multiscale Fisher's independence test (MULTIFIT hereafter) proposed by Gorsky & Ma (2022) is a novel method to test independence between two random vectors. By its design, this test is particularly useful in detecting local dependence. Moreover, by adopting a resampling-free approach, it can easily accommodate massive sample sizes. Another benefit of the proposed method is its ability to interpret the nature of dependency. We congratulate the authors, Shai Gorksy and Li Ma, for their very interesting and elegant work. In this comment, we would like to discuss a general framework unifying the MULTIFIT and other tests and compare it with the binary expansion randomized ensemble test (BERET hereafter) proposed by Lee et al. (In press). We also would like to contribute our thoughts on potential extensions of the method.