Understanding which parts of a dynamical system cause each other is extremely relevant in fundamental and applied sciences. However, inferring causal links from observational time series data, namely without direct manipulations of the system, is still computationally challenging, especially if the data are high-dimensional.
In the first part of this seminar, I will introduce a novel approach for inferring the presence of causal relationships from high-dimensional time series data, based on the minimisation of the Information Imbalance measure. Then, I will show how this approach can be used to infer causality between collective variables extracted from molecular dynamics, and under which hypothesis a correct causal inference is achievable.
In the second part of the seminar, I will extend the proposed measure to tackle the problem of causal network reconstruction, introducing an algorithm whose computational cost scales linearly with the number of variables. The approach is based on the automatic identification of dynamical communities, groups of variables which mutually influence each other and can therefore be described as a single node in a causal graph. These communities are naturally ordered starting from the fully autonomous ones, whose evolution is independent from all the others, to those that are progressively dependent on other communities. This framework provides an efficient and promising alternative for analyzing high-dimensional systems where all-variable time series graphs become unmanageable.