Deep learning has achieved great progress in speech processing, language processing and computer vision. In other applications, however, we often have to work with signals defined on graphs rather than grids. Recently there has been a lot of interest in trying to apply deep learning to graph-based data, as models of this kind can capture the interactions between components in real-world networks.

In current thesis, I address the task of node classification and link prediction on large graphs. I use a variational autoencoder with different graph convolutional layers, including a novel layer based on the Lanczos algorithm. The capability of the proposed architecture is confirmed in various numerical experiments.

I also investigate two possible applications related to bioinformatics. In one task, I perform gene ontology classification based on the human protein-protein interaction network. I show that the autoencoder successfully reconstructs the data, and the latent variables are powerful predictors of gene ontologies. In the other task, I attempt to predict multiple types of molecular interactions. I hypothesise that newly constructed links are newly discovered connections, and I look for literature evidence to reinforce my hypothesis.

Evaluation confirms that by applying graph convolutions, we can accomplish the most important graph-related modeling tasks, and the proposed architecture is able to provide state-of-the-art results. Code is available here.