Semi supervised learning struggles with uneven spatial data sampling
Semi-Supervised Learning under Spatially Biased Sampling
Machine Learning
Summary
Semi-supervised learning is a method that tries to learn from both labeled and unlabeled data. This paper looks at what happens when the labeled data comes from only certain locations, causing the data to be uneven or biased in space. The researchers found that this unevenness can cause the learning process to suddenly fail instead of gradually worsening. They also showed that the problem is made worse by changes in the data’s behavior across different locations and that models become too confident in areas without labels. The paper offers tools to detect when this spatial bias is causing trouble in these learning methods.
semi-supervised learningspatial biasdistribution mismatchspatial autocorrelationspatial non-stationaritycluster assumptionmanifold assumptiondistribution divergencelabeled and unlabeled datachangepoint analysis
Authors
Bright Wiredu Nuakoh, Francky Fouedjio, Stephen Bradshaw, Yaw Kwaafo Awuah-Mensah, Wei Hong Tan, Emet Arya, Ebenezer Afrifa-Yamoah
Abstract
Standard semi-supervised learning (SSL) typically relies on labelled and unlabelled data sharing a common marginal distribution. This assumption is often violated by biased spatial sampling mechanism, when labels are collected under spatially biased or preferential site selection. We treat this marginal mismatch, spatial autocorrelation, and spatial non-stationarity as three distinct mechanisms, varied independently via a labelled-sampling concentration parameter, a spatial length scale, and a non-stationarity strength parameter, and ask how mismatch degrades SSL, whether the cluster and manifold assumptions survive it, and how the resulting failure can be diagnosed. Using a controlled synthetic framework alongside PovertyMap-WILDS, California housing, socio-economic and US air quality monitoring datasets, we systematically vary the degree of mismatch while accounting for spatial autocorrelation and non-stationarity. Through a series of analyses including a segmented-regression changepoint, we show that in the synthetic generator, SSL performance does not degrade gradually but instead exhibits a threshold-like breakdown between approximately 0.71 and 0.77 once distribution mismatch becomes sufficiently severe. We further demonstrate that spatial non-stationarity contributes to performance loss independently of marginal mismatch and that models become increasingly overconfident outside the regions where labels are available. To support practical deployment, we evaluate several distribution-divergence measures as indicators of reliability and introduce a kernel-weighted local divergence metric that provides a more stable estimate of spatial mismatch than a naïve localised approach. These findings provide empirical evidence and diagnostic tools for better documenting the risk of incorporating unlabelled spatial data into semi-supervised learning workflows.