Causality, Information, and Decision-Making

Causal models capture essential aspects of how we conceptualize the world and make decisions about intervening on it. Accordingly, their study has become a central topic in current artificial intelligence research. There are numerous challenges in causality, including problems where the causal model is not known and must be inferred from data, and also problems where the model is known. In this thesis, we focus on the latter case, where (a part of) the causal model is available, and our goal is to extract information about the system and/or simplify parts of the causal model to reveal insights and facilitate decision-making. We approach this goal in three ways. Firstly, we propose and formally study causal versions of information theoretical quantities, including causal entropy, causal information gain, conditional causal entropy, and conditional causal information gain. These new quantities aim to establish a foundation for information-based methods in explainable artificial intelligence (XAI), where information-based methods are prevalent but often fail to incorporate causality, limiting their ability to provide causal insights. Secondly, we extend the information bottleneck method, a widely used approach for learning compressive abstractions of variables while preserving statistical information about a target, by incorporating causality. We utilize causal information gain to develop this causal information bottleneck method, which learns abstractions that provide insights into the causal relationships between the compressed variables and the target variable, even in cases where the functional relationships between variables are unknown. Finally, we leverage knowledge of the causal graph to simplify a decision-theoretical problem, specifically the multi-armed bandit problem where an action is a conditional intervention on the causal graph. We devise a graphical characterization of the minimal search space and an efficient algorithm to find it, thereby reducing the complexity of the decision-making process. This thesis contributes to the field of causal machine learning by providing innovative tools and methodologies that enhance causal interpretability and facilitate effective decision-making.