A distance‐based framework for causal discovery from high‐dimensional time series

Unveiling causal relationships between time-dependent variables, observed as time series, is a challenge with countless applications across diverse scientific fields. This task lies at the heart of a research area known as causal discovery. In this thesis, we introduce a framework for causal discovery which is based on the quantification of the information content of different distance measures, built with suitable subsets of the observed variables. Focusing on distances, rather than directly on the variables, offers significant advantages when applied to high-dimensional systems. The most important advantage is a strongly enhanced statistical power in detecting when a causal link is absent, which brings to a reduced rate of false positive detections. After benchmarking our approach on chaotic dynamical systems and real-world electroencephalographic data, we apply it to the study of causality in physical systems described by molecular dynamics simulations, in a setting in which the system explores a stationary equilibrium distribution. We show that even in these conditions genuine causal links can emerge. In this context, we interpret the emergence of unidirectional causal links between specific collective variables in terms of the structure of the free energy landscapes. We find that a prerequisite for the existence of causal links in molecular systems is a significant separation of the time scales. Furthermore, we propose to identify causal relationships in molecular systems using computational experiments that mimic ideal manipulations of the collective variables of interest. Finally, we build upon our distance-based framework to tackle the problem of causal graph reconstruction, by proposing an algorithm that outputs a "mesoscopic" version of standard causal graphs, where groups of variables are aggregated into single nodes. We show that this framework carries both computational and conceptual advantages, on the one hand simplifying the inference process, and on the other hand yielding a more compact and interpretable causal graph.