Generalised temporal network inference

Network inference is becoming increasingly central in the analysis of complex phenomena as it allows to obtain understandable models of entities interactions. Among the many possible graphical models, Markov Random Fields are widely used as they are strictly connected to a probability distribution assumption that allow to model a variety of different data. The inference of such models can be guided by two priors: sparsity and non-stationarity. In other words, only few connections are necessary to explain the phenomenon under observation and, as the phenomenon evolves, the underlying connections that explain it may change accordingly. This thesis contains two general methods for the inference of temporal graphical models that deeply rely on the concept of temporal consistency, i.e., the underlying structure of the system is similar (i.e., consistent) in time points that model the same behaviour (i.e., are dependent). The first contribution is a model that allows to be flexible in terms of probability assumption, temporal consistency, and dependency. The second contribution studies the previously introduces model in the presence of Gaussian partially un-observed data. Indeed, it is necessary to explicitly tackle the presence of un-observed data in order to avoid introducing misrepresentations in the inferred graphical model. All extensions are coupled with fast and non-trivial minimisation algorithms that are extensively validate on synthetic and real-world data. Such algorithms and experiments are implemented in a large and well-designed Python library that comprehends many tools for the modelling of multivariate data. Lastly, all the presented models have many hyper-parameters that need to be tuned on data. On this regard, we analyse different model selection strategies showing that a stability-based approach performs best in presence of multi-networks and multiple hyper-parameters