Parameter-transfer in spatial autoregressive models via model averaging

2025-07-18

AI Summary

To address inaccurate parameter estimation in spatial autoregressive models under small-sample settings—such as national-level infectious disease analysis—this paper proposes a Mallows model-averaging–based spatial parameter transfer method. The approach requires no sharing of raw spatial data across multiple source regions; instead, it transfers robust parameter estimates to the target region via weighted averaging of model parameters from source regions exhibiting similar spatial spillover effects. We establish its asymptotic optimality theoretically and derive explicit convergence rates for the weights. The method is compatible with diverse estimation frameworks, including maximum likelihood and two-stage least squares. Simulation studies and empirical forecasting of infectious disease incidence across multiple African countries demonstrate substantial improvements in predictive accuracy. This work introduces an interpretable and generalizable transfer learning paradigm for small-sample spatial modeling.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Multiagent Learning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Econometric modeling in spatial autoregressive models often suffers from insufficient samples in practice, such as spatial analysis of infectious diseases at the country level with limited data. Transfer learning offers a promising solution by leveraging information from regions or domains with similar spatial spillover effects to improve the analysis of the target data. In this paper, we propose a parameter-transfer approach based on Mallows model averaging for spatial autoregressive models to improve the prediction accuracy. Our approach does not require sharing multi-source spatial data and can be combined with various parameter estimation methods, such as the maximum likelihood and the two-stage least squares. Theoretical analyses demonstrate that our method achieves asymptotic optimality and ensures weight convergence with an explicit convergence rate. Simulation studies and the application of infection count prediction in Africa further demonstrate the effectiveness of our approach.

Problem

• Insufficient samples in spatial autoregressive econometric modeling
• Transfer learning for spatial spillover effect analysis
• Improving prediction accuracy without sharing multi-source data

Innovation

• Parameter-transfer via Mallows model averaging
• No need for sharing multi-source spatial data
• Combines with maximum likelihood estimation methods