While graph neural networks (GNNs) are widely used for node and graph representation learning tasks, the reliability of GNN uncertainty estimates under distribution shifts remains relatively under-explored. Indeed, while post-hoc calibration strategies can be used to improve in-distribution calibration, they need not also improve calibration under distribution shift. However, techniques which produce GNNs with better intrinsic uncertainty estimates are particularly valuable, as they can always be combined with post-hoc strategies later. Therefore, in this work, we propose G-$\Delta$UQ, a novel training framework designed to improve intrinsic GNN uncertainty estimates. Our framework adapts the principle of stochastic data centering to graph data through novel graph anchoring strategies, and is able to support partially stochastic GNNs. While, the prevalent wisdom is that fully stochastic networks are necessary to obtain reliable estimates, we find that the functional diversity induced by our anchoring strategies when sampling hypotheses renders this unnecessary and allows us to support G-$\Delta$UQ on pretrained models. Indeed, through extensive evaluation under covariate, concept and graph size shifts, we show that G-$\Delta$UQ leads to better calibrated GNNs for node and graph classification. Further, it also improves performance on the uncertainty-based tasks of out-of-distribution detection and generalization gap estimation. Overall, our work provides insights into uncertainty estimation for GNNs, and demonstrates the utility of G-$\Delta$UQ in obtaining reliable estimates.

Generalized additive models (GAMs) have become a leading model class for data bias discovery and model auditing. However, there are a variety of algorithms for training GAMs, and these do not always learn the same things. Statisticians originally used splines to train GAMs, but more recently GAMs are being trained with boosted decision trees. It is unclear which GAM model(s) to believe, particularly when their explanations are contradictory. In this paper, we investigate a variety of different GAM algorithms both qualitatively and quantitatively on real and simulated datasets. Our results suggest that inductive bias plays a crucial role in model explanations and tree-based GAMs are to be recommended for the kinds of problems and dataset sizes we worked with.