Research

tl;dr: In a nutshell, I utilize methods from decision and game theory as well as the theory of imprecise probabilities to make machine learning (ML) methods more reliable and robust to their implicit assumptions. My work touches on various areas of ML such as uncertainty quantification, trustworthy ML, robust statistical inference and analysis of non-standard data and is published in major ML venues as JMLR, NeurIPS and UAI.

More specifically:

Decision Theoretic Foundations of Machine Learning: On a general level, I am very interested in pretty much everything (even loosely) related to decision making under uncertainty, ranging from axiomatic theories to applications in substance matter contexts. More specifically, I mainly focus on decision-making under weakly structured information, where the weak structure can originate from partially ordered preferences or imprecise probabilistic information or both. Much of my work focuses on developing models formalizing such situations as well as algorithms for efficient decision support. Here, the main focus is always on what can be derived from such generalized modeling for statistical decision theory and machine learning. This is not least due to the fact that decision theory can be understood as a formal superstructure of most common statistical methods.

Optimization Theory: When applying decision theory to real-world problems, e.g. in the context of decision support algorithms and expert systems, optimization theory often plays a crucial role. I have a huge interest in developing new (linear) optimization-based algorithms for determining optimal decisions. Beyond that, I am also very interested in optimization theory and approximation theory from a purely theoretical point of view.

Stochastic Orderings: Again mainly originating from a decision-theoretic point of view, I am also very fascinated by stochastic orderings. When generalizing optimality criteria from classical decision theory to more complexly structured information settings, there often arise very nice and natural generalizations of classical stochastic orderings like e.g., (first-order) stochastic dominance or statistical preference. These generalizations then can be re-adapted to e.g. statistical contexts and applications, allowing for completely new perspectives also here.

Imprecise Probabilities: A significant part of my work is concerned with theories for describing and characterizing uncertainty beyond perfect stochasticity. Such theories, commonly summarized under the umbrella term imprecise probability theories, allow for very general models of uncertainty and, accordingly, for flexible and information-efficient descriptions of reality. Here, I am interested in both theoretical aspects (for instance non-additive measures, general integration theory) as well as the huge variety of applications in both Statistics and Decision Theory (for instance Robust Statistics or Choice Models accounting for Ambiguity).