LEARNING, FORECASTING AND CAUSATION AS COMPRESSION.

Two main guidelines can be adopted to investigate a system and forecast its future behavior. The first kind of strategy emphasizes the role of general principles, which guide us in building models that embody the background knowledge available. The second class of techniques refers to phenomena ruled by unknown laws and directly probed by data-driven protocols. While the Scientific Method encodes the first kind of procedure, Data Science embraces more inductive schemes. In the last twenty years, many scholars have developed growing expectations about the impact of the latter family of methods, and the role of inductivism seems to be re-evaluated. This enthusiasm is - to some extent - justified. Despite the numerous successes achieved by model-driven science, many systems seem to resist being understood through a modeling approach. Conversely, valuable advances in performing practical tasks have been obtained by adopting Machine Learning and Pattern Recognition techniques. While a detailed analysis of these protocols' performances is beyond the scope of this discussion, some methodological aspects can be considered on a conceptual level, keeping in the background the possibility of proceeding with formally rigorous arguments. The comparison between modeling and automatic methods will allow for a better framing of the role of intelligence in their respective fields of application. Research Plan. This dissertation starts by examining the properties of a generic database based on simple results from Dynamical Systems. The Analogs Method is considered an archetypal case to illustrate the consequences of an inductivist approach from a broader viewpoint. In this regard, Statistical Learning theory will provide some essential ingredients, allowing us to reformulate the Principle of Induction. This perspective will be elaborated more by using informational language. The compression-generalization trade-off is adopted as a general paradigm, discussing the effectiveness of Deep Learning protocols and drawing parallelisms with coarse-graining procedures. The analysis proposed will naturally lead us to re-read causality as a tool to manage information when some distribution shift comes into play. Moreover, some formal ways of characterizing cause-effect relations will be critically examined, and the potential connections that alternative frameworks may have will be explored to establish a more unified viewpoint. As we critically discuss the challenges inherent in inductive protocols, we aim to shed light on the following general questions. To what extent is mathematical modeling still a necessary pursuit? What role could be played by Artificial Intelligence in this regard?