Dottorato in DATA SCIENCE

Titolo della tesi: Learning Multiscale and Non-stationary Causal Structures: Methods and Applications

Learning causal relationships from observational data is a crucial task whenever interventional approaches are unfeasible or unethical. Existing causal structure learning methods assume that causal relationships can occur only at the observed data frequency, without taking into account the possibility that different causal relationships may arise at different time scales: the present thesis moves a first step to tackle this major limitation. In this regard, this thesis provides three main methodological contributions. The first key contribution is the Multiscale Causal Structure Learning (MS-CASTLE) method. Hinging on stationary wavelet transform and non-convex optimization, MS-CASTLE learns instantaneous and lagged linear causal relations among multiple time series across different scales. A second methodological contribution is the Multiscale Non-stationary Directed Acyclic Graph (MN-DAG) framework for modeling linear causal relations that are multiscale and non-stationary. We propose a probabilistic generative model over MN-DAGs, and a Bayesian method named Multiscale Non-stationary Causal Structure Learner (MN-CASTLE) that uses stochastic variational inference to learn MN-DAGs. Finally, as a third methodological contribution, this thesis devises two nonconvex methods for learning block-sparse, frequency-dependent, partial correlation graphs to explore linear conditional dependencies between time series occurring at different time scales. The methodological contributions of the thesis are flanked by cutting-edge applications in domains such as finance and neuroscience, showcasing the benefits of learning multiscale and non-stationary causal relationships from time series data.