Distributed Estimation and Inference for Spatial Autoregression Model with Large Scale Networks

TL;DR

This paper introduces a distributed estimation and inference framework for spatial autoregression models on large-scale networks, enabling efficient analysis with theoretical guarantees and practical validation on real data.

Contribution

It develops a novel distributed estimation method with bias reduction and a communication-efficient inference procedure for large-scale SAR models.

Findings

The estimators are consistent and asymptotically normal.

The methods are computationally efficient and scalable.

Validation on real data demonstrates practical effectiveness.

Abstract

The rapid growth of online network platforms generates large-scale network data and it poses great challenges for statistical analysis using the spatial autoregression (SAR) model. In this work, we develop a novel distributed estimation and statistical inference framework for the SAR model on a distributed system. We first propose a distributed network least squares approximation (DNLSA) method. This enables us to obtain a one-step estimator by taking a weighted average of local estimators on each worker. Afterwards, a refined two-step estimation is designed to further reduce the estimation bias. For statistical inference, we utilize a random projection method to reduce the expensive communication cost. Theoretically, we show the consistency and asymptotic normality of both the one-step and two-step estimators. In addition, we provide theoretical guarantee of the distributed statistical inference procedure. The theoretical findings and computational advantages are validated by several numerical simulations implemented on the Spark system. Lastly, an experiment on the Yelp dataset further illustrates the usefulness of the proposed methodology.