  Machine learning models that embed graphs in non-Euclidean spaces have shown
substantial benefits in a variety of contexts, but their application has not
been studied extensively in the biological domain, particularly with respect to
biological pathway graphs. Such graphs exhibit a variety of complex network
structures, presenting challenges to existing embedding approaches. Learning
high-quality embeddings for biological pathway graphs is important for
researchers looking to understand the underpinnings of disease and train
high-quality predictive models on these networks. In this work, we investigate
the effects of embedding pathway graphs in non-Euclidean mixed-curvature spaces
and compare against traditional Euclidean graph representation learning models.
We then train a supervised model using the learned node embeddings to predict
missing protein-protein interactions in pathway graphs. We find large
reductions in distortion and boosts on in-distribution edge prediction
performance as a result of using mixed-curvature embeddings and their
corresponding graph neural network models. However, we find that
mixed-curvature representations underperform existing baselines on
out-of-distribution edge prediction performance suggesting that these
representations may overfit to the training graph topology. We provide our
mixed-curvature product GCN code at
https://github.com/mcneela/Mixed-Curvature-GCN and our pathway analysis code at
https://github.com/mcneela/Mixed-Curvature-Pathways.
