改进地理加权回归的模型偏差,提升复杂空间关系建模能力。
Rethinking Inductive Bias in Geographically Neural Network Weighted Regression
- 引入卷积、循环和注意力机制增强空间权重学习
- 在异质性数据上表现优于传统方法,小样本场景更优
- 适合处理非平稳空间数据的科研与城市规划人员
归纳偏置是空间回归模型的关键因素,决定模型在有限数据下学习和捕捉空间模式的能力。本文重新审视地理神经网络加权回归(GNNWR)中的归纳偏置,发现现有方法在建模空间非平稳性方面存在局限。尽管GNNWR通过神经网络学习空间权重函数扩展了传统地理加权回归,但其仍受限于固定距离方案和有限的归纳偏置。我们提出通过引入卷积神经网络、循环神经网络和Transformer的思想,将局部感受野、序列上下文和自注意力机制融入空间回归。在具有不同异质性、噪声水平和样本量的合成空间数据集上进行广泛基准测试表明,GNNWR在捕捉非线性和复杂空间关系方面优于经典方法。结果还显示,模型性能高度依赖数据特征:局部模型在高异质性或小样本场景中表现更佳,全局模型则在大规模、同质数据中表现更好。这些发现强调了归纳偏置在空间建模中的重要性,并指明未来方向,包括可学习的空间权重函数、混合神经架构以及提升对非平稳空间数据模型的可解释性。
原文摘要 · Abstract (English)
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.
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