Randomized algorithms of maximum likelihood estimation with spatial autoregressive models for large-scale networks

Abstract

The spatial autoregressive (SAR) model is a classical model in spatial econometrics and has become an important tool in network analysis. However, with large-scale networks, existing methods of likelihood-based inference for the SAR model become computationally infeasible. We here investigate maximum likelihood estimation for the SAR model with partially observed responses from large-scale networks. By taking advantage of recent developments in randomized numerical linear algebra, we derive efficient algorithms to estimate the spatial autocorrelation parameter in the SAR model. Compelling experimental results from extensive simulation and real data examples demonstrate empirically that the estimator obtained by our method, called the randomized maximum likelihood estimator, outperforms the state of the art by giving smaller bias and standard error, especially for large-scale problems with moderate spatial autocorrelation. The theoretical properties of the estimator are explored, and consistency results are established.