TOWARDS THE ESTIMATION OF CAUSAL NETWORKS BY THE INFORMATION IMBALANCE APPROACH

Inferring the presence of causal links from observational data is a challenging task which typically goes under the name of causal discovery. After reviewing the basic concepts of this field and a standard algorithm used to infer the topology of causal graphs, we develop an approach specifically designed for times series data based on the Information Imbalance measure. This estimator, first introduced by Glielmo et al., 2022 for ranking the information content of different distance spaces, has been applied by Del Tatto et al., 2024 to detect causal relationships between time-dependent variables. Recently, it has been reformulated in a differentiable version (Wild et al., 2024) which allows the automatic learning of the most informative distance function in a gradient-descent fashion. In the first part of this thesis, we further extend this measure, introducing a procedure to estimate its statistical error. We then use this measure in a framework for causal network reconstruction from time series data. Specifically, we define a protocol to progressively find subsets of independent variables in complex non-linear dynamical systems. This allows generating a macroscopic acyclic graph showing the hierarchy of the interactions between different groups of features of the dataset. In contrast with standard causal discovery methods, the algorithm proposed here does not require any combinatorial search of conditioning sets, can be also applied to high-dimensional systems and intrinsically retrieves multi-body interactions.