Section: Research Program

General presentation

Our objectives correspond to four major challenges of machine learning where mathematical statistics have a key role. First, any machine learning procedure depends on hyperparameters that must be chosen, and many procedures are available for any given learning problem: both are an estimator selection problem. Second, with high-dimensional and/or large data, the computational complexity of algorithms must be taken into account differently, leading to possible trade-offs between statistical accuracy and complexity, for machine learning procedures themselves as well as for estimator selection procedures. Third, real data are almost always corrupted partially, making it necessary to provide learning (and estimator selection) procedures that are robust to outliers and heavy tails, while being able to handle large datasets. Fourth, science currently faces a reproducibility crisis, making it necessary to provide statistical inference tools (p-values, confidence regions) for assessing the significance of the output of any learning algorithm (including the tuning of its hyperparameters), in a computationally efficient way.