Acknowledging the structured nature of real-world data with graphs embeddings and probabilistic inference methods

In the artificial intelligence community there is a growing consensus that real world data is naturally represented as graphs because they can easily incorporate complexity at several levels, e.g. hierarchies or time dependencies. In this context, this thesis studies two main branches for structured data. In the first part we explore how state-of-the-art machine learning methods can be extended to graph modeled data provided that one is able to represent graphs in vector spaces. Such extensions can be applied to analyze several kinds of real-world data and tackle different problems. Here we study the following problems: a) understand the relational nature and evolution of websites which belong to different categories (e-commerce, academic (p.a.) and encyclopedic (forum)); b) model tennis players scores based on different game surfaces and tournaments in order to predict matches results; c) analyze preter- m-infants motion patterns able to characterize possible neuro degenerative disorders and d) build an academic collaboration recommender system able to model academic groups and individual research interest while suggesting possible researchers to connect with, topics of interest and representative publications to external users. In the second part we focus on graphs inference methods from data which present two main challenges: missing data and non-stationary time dependency. In particular, we study the problem of inferring Gaussian Graphical Models in the following settings: a) inference of Gaussian Graphical Models when data are missing or latent in the context of multiclass or temporal network inference and b) inference of time-varying Gaussian Graphical Models when data is multivariate and non-stationary. Such methods have a natural application in the composition of an optimized stock markets portfolio. Overall this work sheds light on how to acknowledge the intrinsic structure of data with the aim of building statistical models that are able to capture the actual complexity of the real world.