Predictive relevance in dynamical systems

Complex systems have been the object of studies across diverse fields, comprising both hard and soft sciences. The data revolution and the enormous amount of data available in recent years allowed for their quantitative analysis. According to the problem under investigation, one can focus on their stationary properties, thus adopting a static description, or analyze their dynamics and their out-of-equilibrium properties. The goal of this thesis is to investigate the dynamical behavior of a complex system using dimensional reduction, a technique aiming to reduce the number of degrees of freedom of the system by constructing a synthetic, more effective representation. Here we focus on a fully unsupervised approach to dimensional reduction by coupling clustering techniques with recent ideas of maximally informative representations. The performance of prediction algorithms built around these ideas has been tested. The relation between prediction power and information content, of the clustering label set, has been examined by considering two numerical experiments. The first experiment is designed for finding the best agglomerative methods' inter-cluster linkage, while the second experiment for investigating whether, starting from a system state representation, it has been possible to detect time series underlying generative model properties. The experimental results have been used for drawing general conclusions about this dimensional reduction technique.