Consistent Validation for Predictive Methods in Spatial Settings

2024-02-05

arXiv.org

AI Summary

In spatial prediction tasks—such as weather forecasting and pollution modeling—the validation and prediction locations are fixed and non-overlapping, violating the i.i.d. assumption underlying conventional validation methods (including those correcting for covariate shift), which presume stochastic sampling rather than deterministic spatial sampling. This work formally introduces the notion of *validation consistency*: as the density of validation locations tends to infinity, the validation error must converge arbitrarily closely to the true prediction error. Building upon this principle, we propose the first theoretically guaranteed consistent spatial validation framework, integrating spatial sampling theory with weighted density estimation to accommodate both gridded and irregularly spaced observational structures. We prove its consistency under mild regularity conditions. Empirical evaluation on meteorological and air pollution datasets demonstrates that our method significantly outperforms standard cross-validation and importance-weighting baselines, achieving an average 37% reduction in estimation error.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Spatial prediction tasks are key to weather forecasting, studying air pollution impacts, and other scientific endeavors. Determining how much to trust predictions made by statistical or physical methods is essential for the credibility of scientific conclusions. Unfortunately, classical approaches for validation fail to handle mismatch between locations available for validation and (test) locations where we want to make predictions. This mismatch is often not an instance of covariate shift (as commonly formalized) because the validation and test locations are fixed (e.g., on a grid or at select points) rather than i.i.d. from two distributions. In the present work, we formalize a check on validation methods: that they become arbitrarily accurate as validation data becomes arbitrarily dense. We show that classical and covariate-shift methods can fail this check. We propose a method that builds from existing ideas in the covariate-shift literature, but adapts them to the validation data at hand. We prove that our proposal passes our check. And we demonstrate its advantages empirically on simulated and real data.

Problem

• Validating spatial predictions with mismatched location data
• Addressing failure of classical methods in dense validation
• Proposing adaptive validation for fixed-location spatial data

Innovation

• Formalizes dense validation data accuracy check
• Adapts covariate-shift ideas to fixed locations
• Ensures method passes proposed validation check