Crawling subsampling for multivariate spatial autoregression model in large-scale networks

Abstract

In network data analysis, multivariate spatial autoregression (MSAR) models may be used to analyze the autocorrelation among multiple responses. With large-scale networks, the estimation for MSAR on the entire network is computationally expensive. In this case, the subsampling method could be adopted. This approach selects a sample of nodes and then uses the estimate based on the sample to approximate the estimate on the full data. However, traditional sampling methods cannot obtain unbiased parameter estimates. Considering the second-order friend information of sampled nodes, we propose the crawling subsampling (CS) method for a general framework. Thereafter, based on the sampled data only, we construct the least-squares objective function. Under certain conditions, the computational complexity of optimizing the objective function is linear with the sample size ns. The identification condition for the parameters on the sampled network is theoretically provided. The sample size order requirement is provided, and the asymptotic properties of the least-squares estimators are investigated. The numerical results for the simulated and real data are presented to demonstrate the performance of the proposed CS method and least-squares estimator for the MSAR model.

Community Network Auto-Regression for High-Dimensional Time Series

“…Particularly, the network effect β 1 reflects the influence of connected nodes through their averages at time t − 1, and the momentum effect β 2 quantifies the autoregressive effects from the same node. The NAR model and its variants have been applied to a wide range of fields, such as social behavior studies (Sojourner, 2013;Liu et al, 2017;Zhu et al, 2018), financial risk management (Härdle et al, 2016;Zou et al, 2017), spatial data modeling (Lee and Yu, 2009;Shi and Lee, 2017), among others.…”

“…and Sojourner (2013); Liu et al (2017); Zhu et al (2018) consider the multivariate responses. However, previous researches do not fully address two important issues that arise commonly in real applications, namely, heterogeneous network effect and unknown cross-sectional dependence.…”