Central goal of the research group is to develop computationally-scalable and mathematically-justified methodologies for “small sample grey-box learning” combined with big data analysis challenges, enabling to obtain valid results even by learning from a few examples only. In recent years, the small data challenges emerging in various applications, particularly in biomedicine, in geosciences and in economics/finance, have indicated an urgent need for replacing the current state-of-the-art data-hungry AI and ML tools with algorithms that can smartly handle available information and are still statistically valid with fewer data. The group of Illia Horenko develops several “grey-box” small data analysis algorithms on the boundary between ML and applied mathematics, based on a joint mathematical formulation of an entropy-optimal feature selection, Bayesian label-matching and sparse probabilistic data approximation. The research group is advancing these algorithms with data sets from different disciplines, including biomedicine, finance and geosciences. In contrast to the state-of-the-art in ML, these methods do not solve distinct data analysis steps sequentially in a pipeline but solve all of these problems jointly and simultaneously based on a scalable numerical solution of the appropriate optimal discretization problem. They allow obtaining geometrically-interpretable models trained with numerical optimization algorithms with linear computational cost scaling. Furthermore, these methods are characterized by mathematically-justified regularity and optimality of the obtained solutions and a parallel communication cost proven to be independent of the sample statistics size.