## Research interests

The research group "Mathematical Statistics & Machine Learning" headed by Prof. Dr. Alexandra Carpentier is part of the Institute of Mathematical Stochastics, Department of Mathematics, Otto-von-Guericke University Magdeburg. We are focusing on problems in mathematical statistics and machine learning :

- In mathematical statistics, the main research interest of our group is composite-composite testing problems, where we aim at understanding which properties of the statistical hypotheses drive the minimax separation rate between the hypotheses so that a non-trivial test exists. Specific examples of a such questions are crucial for uncertainty quantification in high and infinite dimensional models. We also study problems of adaptive inference in different settings, e.g. for matrix completion and extreme value theory.
- In machine learning, the main research interest of our group is sequential sampling, and in particular sequential and adaptive sampling problems related to the bandit problem. We study active strategies and their theoretical performance, and are interested in constructing algorithms that are efficient in a minimax optimal sense.
- We combine our two demain of research in order to consider sequential learning on complex systems, and focus in particular on the problem of adapting sequential strategy to the model generating the data, using elements from adaptive inference and uncertainty quantification.

### Keywords

Anomaly detection, High or Infinite-Dimensional Statistical Inference, Inverse Problems and Compressed Sensing, Adaptive Estimation and Confidence Sets, Uncertainty quantification, Sequential Sampling, Bandit Theory, Optimisation of Computational Resources, Matrix Completion, Extreme Value Theory, Applications in Engineering, Neuroscience and Quantum Physic.

### Acknowledgements

Alexandra Carpentier is an Emmy Noether research group leader for the project MuSyAD (CA 1488/1-1), funded by the Deutsche Foschungsgemeinschaft (DFG, German Research Foundation), and Andrea Locatelli and Maurilio Gutzeit are funded by this project. The group is also funded by the Deutsche Foschungsgemeinschaft (DFG, German Research Foundation) on the GK 2297 MathCoRe on “Mathematical Complexity Reduction" 314838170, GRK 2297 MathCoRe, and by the SFB 1294 Data Assimilationon “Data Assimilation, The seamless integration of data and models", Project A03, where Alexandra Carpentier is a PI.