AI in Mathematics Group

Welcome to the AI in Mathematics Group


The AI in Mathematics Group

Welcome to the website of the AI in Mathematics group in the Department of Mathematics at RPTU Kaiserslautern-Landau. This group was newly founded within the framework of the AI initiative of the state of Rhineland-Palatinate and is still under development.

 

Address

AG KI in der Mathematik
Gottlieb-Daimler-Straße
Gebäude 48 , Raum 514
67663 Kaiserslautern

Postfach 3049
67653 Kaiserslautern

Prof. Dr. Illia Horenko

Tel.: +49 631 205 5060
Fax: +49 631 205 4427
E-Mail: horenko@mathematik.uni-kl.de

Research Interests

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.

Competence Areas

  • Mathematical Methods and Computational Tools for the “small data“ Learning Challenge
  • Methods for Computational Time Series Analysis of Real-Life Systems
  • Mathematical Foundations of AI
  • Biomedical Simulations
  • Data Analysis
  • Parallel Large-scale Simulations of Biological and Physical Systems
  • Weather Simulations

"Small Data" Learning Tools

Links to our open-source software tools for “small data” learning:

Links to research groups using our “small data” learning tools:

 

 

 

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