Rethinking Inductive Bias in Geographically Neural Network Weighted Regression

TL;DR

This paper reexamines and enhances the inductive biases in Geographically Neural Network Weighted Regression by integrating neural network architectures like CNNs, RNNs, and transformers to better model complex spatial patterns, especially in heterogeneous data.

Contribution

It introduces a generalized GNNWR framework incorporating advanced neural network concepts, improving modeling of spatial non-stationarity and heterogeneity.

Findings

GNNWR with neural architectures outperforms traditional methods on synthetic datasets.

Local models excel in heterogeneous or small-sample scenarios.

Global models perform better with larger, homogeneous data.

Abstract

Inductive bias is a key factor in spatial regression models, determining how well a model can learn from limited data and capture spatial patterns. This work revisits the inductive biases in Geographically Neural Network Weighted Regression (GNNWR) and identifies limitations in current approaches for modeling spatial non-stationarity. While GNNWR extends traditional Geographically Weighted Regression by using neural networks to learn spatial weighting functions, existing implementations are often restricted by fixed distance-based schemes and limited inductive bias. We propose to generalize GNNWR by incorporating concepts from convolutional neural networks, recurrent neural networks, and transformers, introducing local receptive fields, sequential context, and self-attention into spatial regression. Through extensive benchmarking on synthetic spatial datasets with varying heterogeneity, noise, and sample sizes, we show that GNNWR outperforms classic methods in capturing nonlinear and complex spatial relationships. Our results also reveal that model performance depends strongly on data characteristics, with local models excelling in highly heterogeneous or small-sample scenarios, and global models performing better with larger, more homogeneous data. These findings highlight the importance of inductive bias in spatial modeling and suggest future directions, including learnable spatial weighting functions, hybrid neural architectures, and improved interpretability for models handling non-stationary spatial data.