In the recent years, new tools have been developed for applications of optimal transport in machine learning and statistics, including new tests for classification using Wasserstein distance and statistical properties of Fréchet means of distributions seen as Wasserstein Barycenters. This work has important developments in machine learning for fairness issues and robustness with respect to stress or evolution of distribution for machine learning algorithms.

The main direction of this research project deals with the theoretical properties of statistical inference under fairness constraint modelling how the effect of an algorithm can depend on an unwanted variable whose influence is yet present in the learning sample. A proposition is to rewrite the framework of fair learning using tools from mathematical statistics and optimal transport theory to obtain new methods and bounds (connected to the differential privacy). Extension to others statistical methods (tests, PCA, PLS, matrix factorizations, Bayesian Networks), unsupervised learning and machine learning methods (regression models or ranking models, online algorithms, deep networks, GAN …) can be considered. The goal is to provide new feasible algorithms to promote fairness by adding constraints. Finally, replacing the notion of independence with a notion of causality can provide new ways of understanding algorithms and adding prior knowledge such as acceptability, logic or physical constraints to AI.

The second direction of the research program deals with extensions of fairness models to obtain robust and explainable models. Actually this research on fairness has also other possible impacts by incorporating constraints that guarantee conditional independence with other variables. In features selection, controlling or understanding the real impact of variables and mitigating the unwanted bias coming from unbalanced samples is of high importance in novelty detection or to explain the outcome of algorithms. Then, fairness issues involve understanding the effects of changes in the distribution between the learning sample and the generalization sample. Facing this issue enable to deal with the influence of a change in the distribution for robust machine learning methods or to the presence of multiple distribution for collaborative or consensus inference. Moreover, behaviors of an algorithm under changes of the distributions provides a deep insight on the importance and causality of each variable at play in the learning process. This provides a natural framework to understand global and local explainability of automated rules.

The third direction of the research program is to study biases when the sensitive parameters are unknown. We will focus this study where biases are due to the violation of the independent and identically distributed (i.i.d) hypothesis in unsupervised learning process. In real application, it is commonly assumed that observations in the sample of the dataset are iid which is complex to verify. Wrongly assume i.i.d hypothesis could have undesirable effects like to have poor performance on rare observation or to obtain unfair networks. To avoid to assume i.i.d hypothesis, another assumption could be made: the error of Loss function should be identical regardless of the occurrence of an observation. This new hypothesis is justified in critical system where it’s not only necessaire to have a global good performance but also on rare events. To obtain the distribution of samples, autoregressive models [7] or flow-based models [8] can be used. The first step will be to modify the loss of these models to take into account the new hypothesis.

The fourth direction of the research program will consider theoretical values to extend DP to testing problems (and then classification issues) to evaluate the theoretical cost for privacy. Differential Privacy provides also a theoretical framework that can be used to define a notion of differential fairness where an algorithm behaves similarly for individuals with similar characteristics but different close values for the sensitive variable. Diffential privacy is the most common formalization of the problem of privacy. It can be summed up as the following condition: altering a single data point does not affect the probability of an outcome much. In particular, it can parametrize by some α, where low values of α correspond to a stronger privacy condition.