This habilitation thesis is cumulative and, therefore, is collecting and connecting research that I (together with several co-authors) have conducted over the last few years. Thus, the absolute core of the work is formed by the ten publications listed on page 5 under the name Contributions 1 to 10. The references to the complete versions of these articles are also found in this list, making them as easily accessible as possible for readers wishing to dive deep into the different research projects. The chapters following this thesis, namely Parts A to C and the concluding remarks, serve to place the articles in a larger scientific context, to (briefly) explain their respective content on a less formal level, and to highlight some interesting perspectives for future research in their respective contexts. Naturally, therefore, the following presentation has neither the level of detail nor the formal rigor that can (hopefully) be found in the papers. The purpose of the following text is to provide the reader an easy and high-level access to this interesting and important research field as a whole, thereby, advertising it to a broader audience.

A wide range of machine learning algorithms iteratively add data to the training sample. Examples include semi-supervised learning, active learning, multi-armed bandits, and Bayesian optimization. We embed this kind of data addition into decision theory by framing data selection as a decision problem. This paves the way for finding Bayes-optimal selections of data. For the illustrative case of self-training in semi-supervised learning, we derive the respective Bayes criterion. We further show that deploying this criterion mitigates the issue of confirmation bias by empirically assessing our method for generalized linear models, semi-parametric generalized additive models, and Bayesian neural networks on simulated and real-world data.

We provide a theoretical and computational investigation of the Gamma-Maximin method with soft revision, which was recently proposed as a robust criterion for pseudo-label selection (PLS) in semi-supervised learning. Opposed to traditional methods for PLS we use credal sets of priors ("generalized Bayes") to represent the epistemic modeling uncertainty. These latter are then updated by the Gamma-Maximin method with soft revision. We eventually select pseudo-labeled data that are most likely in light of the least favorable distribution from the so updated credal set. We formalize the task of finding optimal pseudo-labeled data w.r.t. the Gamma-Maximin method with soft revision as an optimization problem. A concrete implementation for the class of logistic models then allows us to compare the predictive power of the method with competing approaches. It is observed that the Gamma-Maximin method with soft revision can achieve very promising results, especially when the proportion of labeled data is low.

Pseudo-Labeling is a simple and effective approach to semi-supervised learning. It requires criteria that guide the selection of pseudo-labeled data. The latter have been shown to crucially affect pseudo-labeling's generalization performance. Several such criteria exist and were proven to work reasonably well in practice. However, their performance often depends on the initial model fit on labeled data. Early overfitting can be propagated to the final model by choosing instances with overconfident but wrong predictions, often called confirmation bias. In two recent works, we demonstrate that pseudo-label selection (PLS) can be naturally embedded into decision theory. This paves the way for BPLS, a Bayesian framework for PLS that mitigates the issue of confirmation bias. At its heart is a novel selection criterion: an analytical approximation of the posterior predictive of pseudo-samples and labeled data. We derive this selection criterion by proving Bayes-optimality of this "pseudo posterior predictive". We empirically assess BPLS for generalized linear, non-parametric generalized additive models and Bayesian neural networks on simulated and real-world data. When faced with data prone to overfitting and thus a high chance of confirmation bias, BPLS outperforms traditional PLS methods. The decision-theoretic embedding further allows us to render PLS more robust towards the involved modeling assumptions. To achieve this goal, we introduce a multi-objective utility function. We demonstrate that the latter can be constructed to account for different sources of uncertainty and explore three examples: model selection, accumulation of errors and covariate shift.

Although being a crucial question for the development of machine learning algorithms, there is still no consensus on how to compare classifiers over multiple data sets with respect to several criteria. Every comparison framework is confronted with (at least) three fundamental challenges: the multiplicity of quality criteria, the multiplicity of data sets and the randomness of the selection of data sets. In this paper, we add a fresh view to the vivid debate by adopting recent developments in decision theory. Based on so-called preference systems, our framework ranks classifiers by a generalized concept of stochastic dominance, which powerfully circumvents the cumbersome, and often even self-contradictory, reliance on aggregates. Moreover, we show that generalized stochastic dominance can be operationalized by solving easy-to-handle linear programs and moreover statistically tested employing an adapted two-sample observation-randomization test. This yields indeed a powerful framework for the statistical comparison of classifiers over multiple data sets with respect to multiple quality criteria simultaneously. We illustrate and investigate our framework in a simulation study and with a set of standard benchmark data sets.

We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies of depth functions in linear and metric spaces, there is very little discussion on depth functions for non-standard data types such as partial orders. We introduce an adaptation of the well-known simplicial depth to the set of all partial orders, the union-free generic (ufg) depth. Moreover, we utilize our ufg depth for a comparison of machine learning algorithms based on multidimensional performance measures. Concretely, we analyze the distribution of different classifier performances over a sample of standard benchmark data sets. Our results promisingly demonstrate that our approach differs substantially from existing benchmarking approaches and, therefore, adds a new perspective to the vivid debate on the comparison of classifiers.

Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to exploit the entire information encoded in them properly. We address this problem by considering an order based on (sets of) expectations of random variables mapping into such non-standard spaces. This order contains stochastic dominance and expectation order as extreme cases when no, or respectively perfect, cardinal structure is given. We derive a (regularized) statistical test for our proposed generalized stochastic dominance (GSD) order, operationalize it by linear optimization, and robustify it by imprecise probability models. Our findings are illustrated with data from multidimensional poverty measurement, finance, and medicine.

The quality of consequences in a decision making problem under (severe) uncertainty must often be compared among different targets (goals, objectives) simultaneously. In addition, the evaluations of a consequence's performance under the various targets often differ in their scale of measurement, classically being either purely ordinal or perfectly cardinal. In this paper, we transfer recent developments from abstract decision theory with incomplete preferential and probabilistic information to this multi-target setting and show how -- by exploiting the (potentially) partial cardinal and partial probabilistic information -- more informative orders for comparing decisions can be given than the Pareto order. We discuss some interesting properties of the proposed orders between decision options and show how they can be concretely computed by linear optimization. We conclude the paper by demonstrating our framework in an artificial (but quite real-world) example in the context of comparing algorithms under different performance measures.

Among the five new tools are one that uses artificial intelligence to help agents answer questions almost instantaneously and one that aggregates information about the customer from disparate data sources. Another makes it easier for customers to authenticate themselves when talking to an agent. The new features will help customer-service agents who are working from home while managing an increased volume of calls about everything from changes to travel plans to inquiries about unemployment benefits, said Larry Augustin, vice president of business applications for Amazon Web Services. The Morning Download delivers daily insights and news on business technology from the CIO Journal team. "The idea is to increase productivity for the agent and increase customer satisfaction for people calling in," Mr. Augustin said.

Neural networks have led to major improvements in image classification but suffer from being non-robust to adversarial changes, unreliable uncertainty estimates on out-distribution samples and their inscrutable black-box decisions. In this work we propose RATIO, a training procedure for Robustness via Adversarial Training on In- and Out-distribution, which leads to robust models with reliable and robust confidence estimates on the out-distribution. RATIO has similar generative properties to adversarial training so that visual counterfactuals produce class specific features. While adversarial training comes at the price of lower clean accuracy, RATIO achieves state-of-the-art $l_2$-adversarial robustness on CIFAR10 and maintains better clean accuracy.