标题： GeoConformal预测：一种衡量空间预测不确定性的模型无关框架 显示英文标题

标题： GeoConformal prediction: a model-agnostic framework of measuring the uncertainty of spatial prediction

摘要： 空间预测是地理学中的基础任务。近年来，随着地理空间人工智能（GeoAI）的进步，许多模型被开发出来以提高地理变量预测的准确性。除了追求更高的精度外，获得带有不确定性度量的预测同样重要，这可以增强模型的可信度并支持负责任的空间预测。尽管地统计方法（如克里金法）提供了一定程度的不确定性评估（如克里金方差），但这些测量值并不总是准确，并且缺乏对其他空间模型的一般适用性。 为了解决这个问题，我们提出了一种名为GeoConformal预测的模型无关的不确定性评估方法，该方法将地理加权纳入到一致性预测中。我们将其应用于两个经典的空 间预测案例，即空间回归和空间插值，以评估其可靠性。首先，在空间回归案例中，我们使用XGBoost预测房价，然后用GeoConformal计算不确定性。我们的结果显示GeoConformal达到了93.67%的覆盖率，而Bootstrap方法在2000次运行后最大覆盖率仅为81.00%。接下来，我们将GeoConformal应用于空间插值模型。我们发现从GeoConformal获得的不确定性与克里金法的方差高度一致。最后，利用GeoConformal，我们分析了空间预测中不确定性的来源。我们发现明确地在AI模型中包含局部特征可以显著减少预测不确定性，尤其是在具有强局部依赖性的区域。我们的研究结果表明，GeoConformal不仅对地理知识发现有潜力，而且可以指导未来GeoAI模型的设计，为更可靠和可解释的空间预测框架铺平道路。 显示英文摘要

摘要： Spatial prediction is a fundamental task in geography. In recent years, with advances in geospatial artificial intelligence (GeoAI), numerous models have been developed to improve the accuracy of geographic variable predictions. Beyond achieving higher accuracy, it is equally important to obtain predictions with uncertainty measures to enhance model credibility and support responsible spatial prediction. Although geostatistic methods like Kriging offer some level of uncertainty assessment, such as Kriging variance, these measurements are not always accurate and lack general applicability to other spatial models. To address this issue, we propose a model-agnostic uncertainty assessment method called GeoConformal Prediction, which incorporates geographical weighting into conformal prediction. We applied it to two classic spatial prediction cases, spatial regression and spatial interpolation, to evaluate its reliability. First, in the spatial regression case, we used XGBoost to predict housing prices, followed by GeoConformal to calculate uncertainty. Our results show that GeoConformal achieved a coverage rate of 93.67%, while Bootstrap methods only reached a maximum coverage of 81.00% after 2000 runs. Next, we applied GeoConformal to spatial interpolation models. We found that the uncertainty obtained from GeoConformal aligned closely with the variance in Kriging. Finally, using GeoConformal, we analyzed the sources of uncertainty in spatial prediction. We found that explicitly including local features in AI models can significantly reduce prediction uncertainty, especially in areas with strong local dependence. Our findings suggest that GeoConformal holds potential not only for geographic knowledge discovery but also for guiding the design of future GeoAI models, paving the way for more reliable and interpretable spatial prediction frameworks.