Optimization Methods for Interpretable Machine Learning

This dissertation is concerned with optimization problems related to transparent machine learning. In the contemporary landscape of machine learning, the importance of interpretability has become essential, resonating across diverse industries and applications. As complex machine learning models, often characterized as "black boxes," continue to demonstrate remarkable predictive capabilities, there arises a pressing need to explain their decision-making processes. Interpretability is crucial not only for building trust in automated systems but also for meeting ethical, legal, and regulatory requirements. In healthcare, interpretable models can offer insights into diagnostic reasoning, aiding healthcare professionals in decision-making and enhancing patient trust. In finance, transparent models are essential for ensuring fair lending practices and regulatory compliance. Legal systems increasingly demand explainability to justify algorithmic decisions, emphasizing the significance of interpretable machine learning in justice. Within this setting,we first briefly describe the most used interpretable models then we discuss novel optimization strategies to handle their learning problem. More precisely, we describe state-of-art approaches to learn decision tree models and, to this aim, we propose two new techniques based to genetic algorithms and mixed integer programming. Afterwards, we present a work on risk score models, enhancing their expressiveness by extending these estimators in a more generalized framework. Finally, in the context of local explanations, we propose a recommendation system for random forest that dinamically maps each point to a single shallow tree in the ensemble.