BCAM Severo Ochoa Course | Machine Learning: the mathematical perspective

Scholarship deadline, May 2nd, 2025

Registration deadline, May 16th, 2025

Santiago Mazuelas' (BCAM) abstract - Day 0 (May 19th)

The course will provide a basic introduction to the mathematics of machine learning with a focus on fairness considerations. The initial day of the course will introduce the main framework for supervised learning and some of the main theoretical results together with common mathematical tools.

Jean-Michel Loubes (INRIA (Institut de Mathématiques de Toulouse)) abstract - Days 1-3 (May 20-22)

As Artificial Intelligence (AI) systems continue to permeate our daily lives, ensuring their fairness has become both a legal necessity and an ethical imperative. This course provides a comprehensive exploration of bias in AI, beginning with core definitions and the evolving legal and regulatory landscape. Participants will investigate how bias originates in data and algorithms, and learn to evaluate and measure it through established fairness metrics. Special emphasis is placed on Optimal Transport (OT) theory and its role in detecting and mitigating bias, both post-hoc ("a posteriori") and before model training ("a priori") or when training ("in-processing"). In addition, the course delves into explaining the underlying causes of bias, enabling practitioners to make AI systems more interpretable. Finally, participants will learn to conduct comprehensive audits of AI algorithms, ensuring these systems adhere to fairness principles. By uniting theoretical constructs, practical tools, and ethical considerations, the course empowers students to develop and deploy AI solutions that promote equitable outcomes for all.

Santiago Mazuelas' lecture references 

• M. Mohri, A. Rostamizadeh, and A. Talwalkar. Foundations of machine learning. MIT press, Cambridge, MA, second edition, 2018
• S. Shalev-Shwartz and S. Ben-David. Understanding machine learning: From theory to algorithms. Cambridge University press, New York, 2014.
• V. Vapnik. Statistical learning theory. Wiley, New York, 1998