BCAM SO Course

I. Introduction to machine learning

• A mathematical theory of induction and empirical risk minimization
• Problem formulation for supervised learning

II. Generalization guarantees 

• Assessing learning performance. The problem of overfitting
• Performance bounds based on uniform convergence of averages. Union bound and Rademacher complexity

Bias in Machine Learning: the mathematical perspective (3h theory) - Jean-Michel Loubes (INRIA (Institut de Mathématiques de Toulouse)

I. A brief survey of Bias in AI

1. Bias definitions

2. What tells the law and the regulation

II. The origin of bias

1. Bias in the data

2. Bias in the algorithm

III. Measures of Bias

IV. Some useful tools: Optimal Transport

Bias in Machine Learning: the mathematical perspective (3h theory) - Jean-Michel Loubes (INRIA (Institut de Mathématiques de Toulouse)

V. Applications of OT to Fairness

1. Detection

2. Bias mitigation

2.1 a posteriori

2.2 a priori

Bias in Machine Learning: the mathematical perspective (4h theory) - Jean-Michel Loubes (INRIA (Institut de Mathématiques de Toulouse))

VI. Explaining Bias

VII. Audit of an algorithm

Santiago Mazuelas is currently an Ikerbasque Research Associate at the Basque Center for Applied Mathematics (BCAM). Prior to joining BCAM, he was a Staff Engineer at Qualcomm R&D from 2014 to 2017, and Postdoctoral Associate in the Laboratory for Information and Decision Systems (LIDS) at the Massachusetts Institute of Technology (MIT) from 2009 to 2014. He is currently Area Chair for the International Conference on Machine Learning (ICML), and associate Editor for two IEEE Transactions. Dr. Mazuelas has received several awards including the Early Achievement Award from the IEEE ComSoc, the IEEE Communications Society Fred W. Ellersick Prize, and the SEIO-FBBVA Best Applied Contribution in the Statistics Field.
 

Abstract:

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.

Bio:

Jean-Michel Loubes (https://perso.math.univ-toulouse.fr/loubes/ ) is a French mathematician and professor specializing in statistics and machine learning. He holds a professorship at the Université Toulouse III - Paul Sabatier and is affiliated with the Institut de Mathématiques de Toulouse (IMT). He is at this moment Research Director at INRIA. His research focuses on mathematical statistics, machine learning, optimal transport, and the fairness and robustness of artificial intelligence systems.

Loubes completed his PhD in Applied Mathematics at Université Toulouse III in 2001, with a dissertation titled "Adaptive M-estimation" under the co-direction of Michel Ledoux and Sara van de Geer. He has held positions as a CNRS researcher at Université Paris-Sud and Université Montpellier II before becoming a professor at Université Toulouse III in 2007.

In addition to his academic roles, Loubes has been actively involved in bridging academia and industry. He served as the regional manager for Occitanie of the CNRS's Agence de Valorisation des Mathématiques (AMIES) from 2010 to 2016.

He is also the holder of the "Fair and Robust Learning" Chair at the Artificial and Natural Intelligence Toulouse Institute (ANITI), where his research addresses issues of fairness and robustness in artificial intelligence.

Throughout his career, Loubes has contributed significantly to the fields of statistics and machine learning, with numerous publications and citations. His work often explores the application of optimal transport theory in machine learning and the development of fair and robust AI systems.

Abstract:

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.