• deep graph networks
• probabilistic models
• hybrid models
• graph learning

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for the adaptive processing of graphs. The dissertation begins with a review of the foundational principles over which most of the methods in the field are built, and the discussion is complemented with a thorough study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. The theoretical framework allows us to consider graphs with both discrete and continuous edge features, and it produces unsupervised embeddings rich enough to reach the state of the art on a number of classification tasks. We later discover that our approach is also amenable to a Bayesian nonparametric extension, which automatizes the choice of almost all models' hyper-parameters. Real-world applications are incorporated into the discussion to demonstrate the efficacy of deep learning for graphs. The first one concerns the prediction of information-theoretic quantities useful in molecular simulations, a problem tackled with supervised neural models for graphs. After that, we exploit our Bayesian models to solve a malware-classification task in such a way that the prediction is robust to intra-procedural code obfuscation techniques. We conclude the dissertation with our attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works in the literature. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.