  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 graph
learning. The dissertation begins with a review of the principles over which
most of the methods in the field are built, followed by a 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. This framework allows us to consider
graphs with discrete and continuous edge features, producing unsupervised
embeddings rich enough to reach the state of the art on several classification
tasks. Our approach is also amenable to a Bayesian nonparametric extension that
automatizes the choice of almost all model's hyper-parameters. Two real-world
applications demonstrate the efficacy of deep learning for graphs. The first
concerns the prediction of information-theoretic quantities for molecular
simulations with supervised neural models. After that, we exploit our Bayesian
models to solve a malware-classification task while being robust to
intra-procedural code obfuscation techniques. We conclude the dissertation with
an 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. Overall, we aim to provide a Bayesian
perspective into the articulated research field of deep learning for graphs.
