Inverse problems applied to blind source separation and fair machine learning

Author(s)

Renan Del Buono Brotto

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação
• Defense date: 2024-08-16

Examining board members

João Marcos Travassos Romano; Charles Casimiro Cavalcante; Mariane Rembold Petraglia; Leonardo Tomazeli Duarte

• Advisor: João Marcos Travassos Romano; Kenji Nose Filho

Abstract

In this work, we apply the ideas about Inverse Problems in Blind Source Separation and Fair Machine Learning. In the first problem, we present two contributions. In the first one, we explored, by using the $\ell_\infty$ norm, the boundedness of the sources' joint probability support. We presend under which conditions the minimum support estimates correspond to the desired sources; we also investigate the developed results by means of numerical simulations. Another contribution to this problem is a generic approach to separate correlated sources, analyzed both theoretically and numerically. Finally, in the second part of this thesis, we present our contribution to Fair Machine Learning. We devoloped a method able to deal with sensitive attributes modeled as continuous-valued variables, such as finnancial condition and skin color. We present some theoretical performance bounds for our approach and we also investigate its performance by using synthetic data, as is tipically used in Econometry problems (AU)

• FAPESP's process: 19/20899-4 - Antisparsity and Equidity in signal processing: from blind source separation to fairness machine learning
• Grantee: Renan Del Buono Brotto
• Support Opportunities: Scholarships in Brazil - Doctorate