  Graph Neural Networks (GNNs) have emerged as potent tools for predicting
outcomes in graph-structured data. Despite their efficacy, a significant
drawback of GNNs lies in their limited ability to provide robust uncertainty
estimates, posing challenges to their reliability in contexts where errors
carry significant consequences. Moreover, GNNs typically excel in
in-distribution settings, assuming that training and test data follow identical
distributions a condition often unmet in real world graph data scenarios. In
this article, we leverage conformal prediction, a widely recognized statistical
technique for quantifying uncertainty by transforming predictive model outputs
into prediction sets, to address uncertainty quantification in GNN predictions
amidst conditional shift\footnote{Representing the change in conditional
probability distribution \(P(label|input)\) from source domain to target
domain.} in graph-based semi-supervised learning (SSL). Additionally, we
propose a novel loss function aimed at refining model predictions by minimizing
conditional shift in latent stages. Termed Conditional Shift Robust (CondSR)
conformal prediction for GNNs, our approach CondSR is model-agnostic and
adaptable to various classification models. We validate the effectiveness of
our method on standard graph benchmark datasets, integrating it with
state-of-the-art GNNs in node classification tasks. Comprehensive evaluations
demonstrate that our approach consistently achieves any predefined target
marginal coverage, enhances the accuracy of state of the art GNN models by up
to 12\% under conditional shift, and reduces the prediction set size by up to
48\%. The code implementation is publicly available for further exploration and
experimentation.
