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Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…
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In robust optimization one seeks to make a decision under uncertainty, where the goal is to find the solution with the best worst-case performance. The set of possible realizations of the uncertain data is described by a so-called…
As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world…
With the introduction of machine learning in high-stakes decision making, ensuring algorithmic fairness has become an increasingly important problem to solve. In response to this, many mathematical definitions of fairness have been…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
When machine learning supports decision-making in safety-critical systems, it is important to verify and understand the reasons why a particular output is produced. Although feature importance calculation approaches assist in…
Understanding the nature of strategic voting is the holy grail of social choice theory, where game-theory, social science and recently computational approaches are all applied in order to model the incentives and behavior of voters. In a…
Calibration measures quantify how much a forecaster's predictions violates calibration, which requires that forecasts are unbiased conditioning on the forecasted probabilities. Two important desiderata for a calibration measure are its…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
Reliable human evaluation is critical to the development of successful natural language generation models, but achieving it is notoriously difficult. Stability is a crucial requirement when ranking systems by quality: consistent ranking of…
We study the numerical stability of the Sherman-Morrison-Woodbury (SMW) identity. Let $B = A + UV^T$ and assume $U$ and $V$ both have full-column rank. We explore error bounds for the SMW identity when we are only able to compute…
We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. The obtained equality indicates that the uncertainty relation can be expressed more accurately, and…
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Max-stability is the property that taking a maximum between two inputs results in a maximum between two outputs. We study max-stability with respect to first-order stochastic dominance, the most fundamental notion of stochastic dominance in…
Quantification of risk positions under model uncertainty is of crucial importance from both viewpoints of external regulation and internal management. The concept of model uncertainty, sometimes also referred to as model ambiguity. Although…