  The development of Machine Learning is experiencing growing interest from the
general public, and in recent years there have been numerous press articles
questioning its objectivity: racism, sexism, \dots Driven by the growing
attention of regulators on the ethical use of data in insurance, the actuarial
community must rethink pricing and risk selection practices for fairer
insurance. Equity is a philosophy concept that has many different definitions
in every jurisdiction that influence each other without currently reaching
consensus. In Europe, the Charter of Fundamental Rights defines guidelines on
discrimination, and the use of sensitive personal data in algorithms is
regulated. If the simple removal of the protected variables prevents any
so-called `direct' discrimination, models are still able to `indirectly'
discriminate between individuals thanks to latent interactions between
variables, which bring better performance (and therefore a better
quantification of risk, segmentation of prices, and so on). After introducing
the key concepts related to discrimination, we illustrate the complexity of
quantifying them. We then propose an innovative method, not yet met in the
literature, to reduce the risks of indirect discrimination thanks to
mathematical concepts of linear algebra. This technique is illustrated in a
concrete case of risk selection in life insurance, demonstrating its simplicity
of use and its promising performance.
