Research Group Eyke Hüllermeier

Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty representation, in particular due to their ability to represent both the aleatoric and epistemic uncertainty in a prediction. However, the design of methods for learning credal set predictors remains a challenging problem. In this paper, we make use of conformal prediction for this purpose. More specifically, we propose a method for predicting credal sets in the classification task, given training data labeled by probability distributions. Since our method inherits the coverage guarantees of conformal prediction, our conformal credal sets are guaranteed to be valid with high probability (without any assumptions on model or distribution). We demonstrate the applicability of our method to natural language inference, a highly ambiguous natural language task where it is common to obtain multiple annotations per example.

Originally rooted in game theory, the Shapley Value (SV) has recently become an important tool in machine learning research. Perhaps most notably, it is used for feature attribution and data valuation in explainable artificial intelligence. Shapley Interactions (SIs) naturally extend the SV and address its limitations by assigning joint contributions to groups of entities, which enhance understanding of black box machine learning models. Due to the exponential complexity of computing SVs and SIs, various methods have been proposed that exploit structural assumptions or yield probabilistic estimates given limited resources. In this work, we introduce shapiq, an open-source Python package that unifies state-of-the-art algorithms to efficiently compute SVs and any-order SIs in an application-agnostic framework. Moreover, it includes a benchmarking suite containing 11 machine learning applications of SIs with pre-computed games and ground-truth values to systematically assess computational performance across domains. For practitioners, shapiq is able to explain and visualize any-order feature interactions in predictions of models, including vision transformers, language models, as well as XGBoost and LightGBM with TreeSHAP-IQ. With shapiq, we extend shap beyond feature attributions and consolidate the application of SVs and SIs in machine learning that facilitates future research.

The partial label ranking (PLR) problem is a supervised learning scenario where the learner predicts a ranking with ties of the labels for a given input instance. It generalizes the well-known label ranking (LR) problem, which only allows for strict rankings. So far, pre-vious learning approaches for PLR have primarily adapted LR methods to accommodate ties in predictions. This paper proposes using multi-output regression (MOR) to address the PLR problem by treating ranking positions as multivariate targets, an approach that has received little attention in both LR and PLR. To effectively employ this approach, we introduce several post-hoc layers that convert MOR results into a ranking, potentially including ties. This framework produces a range of learning approaches, which we demonstrate in experimental evaluations to be competitive with the current state-of-the-art PLR methods.

In this work, we study the influence of domain-specific characteristics when defining a meaningful notion of predictive uncertainty on graph data. Previously, the so-called Graph Posterior Network (GPN) model has been proposed to quantify uncertainty in node classification tasks. Given a graph, it uses Normalizing Flows (NFs) to estimate class densities for each node independently and converts those densities into Dirichlet pseudo-counts, which are then dispersed through the graph using the personalized Page-Rank (PPR) algorithm. The architecture of GPNs is motivated by a set of three axioms on the properties of its uncertainty estimates. We show that those axioms are not always satisfied in practice and therefore propose the family of Committe-based Uncertainty Quantification Graph Neural Networks (CUQ-GNNs), which combine standard Graph Neural Networks (GNNs) with the NF-based uncertainty estimation of Posterior Networks (PostNets). This approach adapts more flexibly to domain-specific demands on the properties of uncertainty estimates. We compare CUQ-GNN against GPN and other uncertainty quantification approaches on common node classification benchmarks and show that it is effective at producing useful uncertainty estimates.

Automated machine learning (AutoML) allows for selecting, parametrizing, and composing learning algorithms for a given data set. While resources play a pivotal role in neural architecture search, it is less pronounced by classical AutoML approaches. In fact, they generally focus on only maximizing predictive quality and disregard the importance of finding resource-efficient solutions. To push resource awareness further, our work explicitly explores how measures such as running time or energy consumption can be better considered in AutoML. Firstly, we propose a novel method for algorithm selection that balances multiple performance aspects (including resource demand) as prioritized by the user with the help of compositional meta-learning. Secondly, to foster research on green meta-learning and AutoML, we release the MetaQuRe data set, which contains information on predictive (Qu)ality and (Re)source consumption of models evaluated across hundreds of data sets and four execution environments. We use this data to put our methodology into practice and conduct an in-depth analysis of how our approach and data set can help in making AutoML more resource-aware, which represents our third contribution. Lastly, we publish MetaQuRe alongside an extensive code base, allowing for reproducing all results, expanding our data with results from custom environments, and exploring MetaQuRe interactively. In short, our work demonstrates both the importance as well as benefits of rethinking AutoML and meta-learning in a resource-aware way, thus paving the path for making future ML solutions more sustainable.

Ensembling a neural network is a widely recognized approach to enhance model performance, estimate uncertainty, and improve robustness in deep supervised learning. However, deep ensembles often come with high computational costs and memory demands. In addition, the efficiency of a deep ensemble is related to diversity among the ensemble members, which is challenging for large, over-parameterized deep neural networks. Moreover, ensemble learning has not yet seen such widespread adoption for unsupervised learning and it remains a challenging endeavor for self-supervised or unsupervised representation learning. Motivated by these challenges, we present a novel self-supervised training regime that leverages an ensemble of independent sub-networks, complemented by a new loss function designed to encourage diversity. Our method efficiently builds a sub-model ensemble with high diversity, leading to well-calibrated estimates of model uncertainty, all achieved with minimal computational overhead compared to traditional deep self-supervised ensembles. To evaluate the effectiveness of our approach, we conducted extensive experiments across various tasks, including in-distribution generalization, out-of-distribution detection, dataset corruption, and semi-supervised settings. The results demonstrate that our method significantly improves prediction reliability. Our approach not only achieves excellent accuracy but also enhances calibration, improving on important baseline performance across a wide range of self-supervised architectures in computer vision, natural language processing, and genomics data.

In dynamic machine learning environments, where data streams continuously evolve, traditional explanation methods struggle to remain faithful to the underlying model or data distribution. Therefore, this work presents a unified framework for efficiently computing incremental model-agnostic global explanations tailored for time-dependent models. By extending static model-agnostic methods such as Permutation Feature Importance, SAGE, and Partial Dependence Plots into the online learning context, the proposed framework enables the continuous updating of explanations as new data becomes available. These incremental variants ensure that global explanations remain relevant while minimizing computational overhead. The framework also addresses key challenges related to data distribution maintenance and perturbation generation in online learning, offering time and memory efficient solutions like geometric reservoir-based sampling for data replacement.

Hyperparameter optimization (HPO) is indispensable for achieving optimal performance in machine learning tasks. A popular class of methods in this regard is based on Successive Halving (SHA), which casts HPO into a pure-exploration multi-armed bandit problem under finite sampling budget constraints. This is accomplished by considering hyperparameter configurations as arms and rewards as the negative validation losses. While enjoying theoretical guarantees as well as working well in practice, SHA comes, however, with several hyperparameters itself, one of which is the maximum budget that can be allocated to evaluate a single arm (hyperparameter configuration). Although there are already solutions to this meta hyperparameter optimization problem, such as the doubling trick or asynchronous extensions of SHA, these are either practically inefficient or lack theoretical guarantees. In this paper, we propose incremental SHA (iSHA), a synchronous extension of SHA, allowing to increase the maximum budget a posteriori while still enjoying theoretical guarantees. Our empirical analysis of HPO problems corroborates our theoretical findings and shows that iSHA is more resource-efficient than existing SHA-based approaches.

In this paper, we formalize the problem of learning coherent collections of decision models, which we call decision catalogues, and illustrate it for the case where models are scoring systems. This problem is motivated by the recent rise of algorithmic decision-making and the idea to improve human decision-making through machine learning, in conjunction with the observation that decision models should be situated in terms of their complexity and resource requirements: Instead of constructing a single decision model and using this model in all cases, different models might be appropriate depending on the decision context. Decision catalogues are supposed to support a seamless transition from very simple, resource-efficient to more sophisticated but also more demanding models. We present a general algorithmic framework for inducing such catalogues from training data, which tackles the learning task as a problem of searching the space of candidate catalogues systematically and, to this end, makes use of heuristic search methods. We also present a concrete instantiation of this framework as well as empirical studies for performance evaluation, which, in a nutshell, show that greedy search is an efficient and hard-to-beat strategy for the construction of catalogues of scoring systems.

The Shapley value (SV) is a prevalent approach of allocating credit to machine learning (ML) entities to understand black box ML models. Enriching such interpretations with higher-order interactions is inevitable for complex systems, where the Shapley Interaction Index (SII) is a direct axiomatic extension of the SV. While it is well-known that the SV yields an optimal approximation of any game via a weighted least square (WLS) objective, an extension of this result to SII has been a long-standing open problem, which even led to the proposal of an alternative index. In this work, we characterize higher-order SII as a solution to a WLS problem, which constructs an optimal approximation via SII and k-Shapley values (k-SII). We prove this representation for the SV and pairwise SII and give empirically validated conjectures for higher orders. As a result, we propose KernelSHAP-IQ, a direct extension of KernelSHAP for SII, and demonstrate state-of-the-art performance for feature interactions.

We warn against a common but incomplete understanding of empirical research in machine learning (ML) that leads to non-replicable results, makes findings unreliable, and threatens to undermine progress in the field. To overcome this alarming situation, we call for more awareness of the plurality of ways of gaining knowledge experimentally but also of some epistemic limitations. In particular, we argue most current empirical ML research is fashioned as confirmatory research while it should rather be considered exploratory.

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.

Over the last decade, the Shapley value has become one of the most widely applied tools to provide post-hoc explanations for black box models. However, its theoretically justified solution to the problem of dividing a collective benefit to the members of a group, such as features or data points, comes at a price. Without strong assumptions, the exponential number of member subsets excludes an exact calculation of the Shapley value. In search for a remedy, recent works have demonstrated the efficacy of approximations based on sampling with stratification, in which the sample space is partitioned into smaller subpopulations. The effectiveness of this technique mainly depends on the degree to which the allocation of available samples over the formed strata mirrors their unknown variances. To uncover the hypothetical potential of stratification, we investigate the gap in approximation quality caused by the lack of knowledge of the optimal allocation. Moreover, we combine recent advances to propose two state-of-the-art algorithms Adaptive SVARM and Continuous Adaptive SVARM that adjust the sample allocation on-the-fly. The potential of our approach is assessed in an empirical evaluation.

We address the problem of uncertainty quantification for graph-structured data, or, more specifically, the problem to quantify the predictive uncertainty in (semi-supervised) node classification. Key questions in this regard concern the distinction between two different types of uncertainty, aleatoric and epistemic, and how to support uncertainty quantification by leveraging the structural information provided by the graph topology. Challenging assumptions and postulates of state-of-the-art methods, we propose a novel approach that represents (epistemic) uncertainty in terms of mixtures of Dirichlet distributions and refers to the established principle of linear opinion pooling for propagating information between neighbored nodes in the graph. The effectiveness of this approach is demonstrated in a series of experiments on a variety of graph-structured datasets.

We present a novel approach to uncertainty quantification in classification tasks based on label-wise decomposition of uncertainty measures. This label-wise perspective allows uncertainty to be quantified at the individual class level, thereby improving cost-sensitive decision-making and helping understand the sources of uncertainty. Furthermore, it allows to define total, aleatoric, and epistemic uncertainty on the basis of non-categorical measures such as variance, going beyond common entropy-based measures. In particular, variance-based measures address some of the limitations associated with established methods that have recently been discussed in the literature. We show that our proposed measures adhere to a number of desirable properties. Through empirical evaluation on a variety of benchmark data sets – including applications in the medical domain where accurate uncertainty quantification is crucial – we establish the effectiveness of label-wise uncertainty quantification.

Medical domain applications require a detailed understanding of the decision making process, in particular when data-driven modeling via machine learning is involved, and quantifying uncertainty in the process adds trust and interpretability to predictive models. However, current uncertainty measures in medical imaging are mostly monolithic and do not distinguish between different sources and types of uncertainty. In this paper, we advocate the distinction between so-called aleatoric and epistemic uncertainty in the medical domain and illustrate its potential in clinical decision making for the case of PET/CT image classification.

Feedback data plays an important role in fine-tuning and evaluating state-of-the-art AI models. Often pairwise text preferences are used: given two texts, human (or AI) annotators select the ‘better’ one. Such feedback data is widely used to align models to human preferences (e.g., reinforcement learning from human feedback), or to rank models according to human preferences (e.g., Chatbot Arena). Despite its wide-spread use, prior work has demonstrated that human-annotated pairwise text preference data often exhibits unintended biases. For example, human annotators have been shown to prefer assertive over truthful texts in certain contexts. Models trained or evaluated on this data may implicitly encode these biases in a manner hard to identify. In this paper, we formulate the interpretation of existing pairwise text preference data as a compression task: the Inverse Constitutional AI (ICAI) problem. In constitutional AI, a set of principles (or constitution) is used to provide feedback and fine-tune AI models. The ICAI problem inverts this process: given a dataset of feedback, we aim to extract a constitution that best enables a large language model (LLM) to reconstruct the original annotations. We propose a corresponding initial ICAI algorithm and validate its generated constitutions quantitatively based on reconstructed annotations. Generated constitutions have many potential use-cases – they may help identify undesirable biases, scale feedback to unseen data or assist with adapting LLMs to individual user preferences. We demonstrate our approach on a variety of datasets: (a) synthetic feedback datasets with known underlying principles; (b) the AlpacaEval dataset of cross-annotated human feedback; and (c) the crowdsourced Chatbot Arena data set.

Properly defining a reward signal to efficiently train a reinforcement learning (RL) agent is a challenging task. Designing balanced objective functions from which a desired behavior can emerge requires expert knowledge, especially for complex environments. Learning rewards from human feedback or using large language models (LLMs) to directly provide rewards are promising alternatives, allowing non-experts to specify goals for the agent. However, black-box reward models make it difficult to debug the reward. In this work, we propose Object-Centric Assessment with Language Models (OCALM) to derive inherently interpretable reward functions for RL agents from natural language task descriptions. OCALM uses the extensive world-knowledge of LLMs while leveraging the object-centric nature common to many environments to derive reward functions focused on relational concepts, providing RL agents with the ability to derive policies from task descriptions.

In settings where only a budgeted amount of labeled data can be afforded, active learning seeks to devise query strategies for selecting the most informative data points to be labeled, aiming to enhance learning algorithms’ efficiency and performance. Numerous such query strategies have been proposed and compared in the active learning literature. However, the community still lacks standardized benchmarks for comparing the performance of different query strategies. This particularly holds for the combination of query strategies with different learning algorithms into active learning pipelines and examining the impact of the learning algorithm choice. To close this gap, we propose ALPBench, which facilitates the specification, execution, and performance monitoring of active learning pipelines. It has built-in measures to ensure evaluations are done reproducibly, saving exact dataset splits and hyperparameter settings of used algorithms. In total, ALPBench consists of 86 real-world tabular classification datasets and 5 active learning settings, yielding 430 active learning problems. To demonstrate its usefulness and broad compatibility with various learning algorithms and query strategies, we conduct an exemplary study evaluating 9 query strategies paired with 8 learning algorithms in 2 different settings.

In this paper, we propose a novel probabilistic self-supervised learning via Scoring Rule Minimization (ProSMIN), which leverages the power of probabilistic models to enhance representation quality and mitigate collapsing representations. Our proposed approach involves two neural networks; the online network and the target network, which collaborate and learn the diverse distribution of representations from each other through knowledge distillation. By presenting the input samples in two augmented formats, the online network is trained to predict the target network representation of the same sample under a different augmented view. The two networks are trained via our new loss function based on proper scoring rules. We provide a theoretical justification for ProSMIN’s convergence, demonstrating the strict propriety of its modified scoring rule. This insight validates the method’s optimization process and contributes to its robustness and effectiveness in improving representation quality. We evaluate our probabilistic model on various downstream tasks, such as in-distribution generalization, out-of-distribution detection, dataset corruption, low-shot learning, and transfer learning. Our method achieves superior accuracy and calibration, surpassing the self-supervised baseline in a wide range of experiments on large-scale datasets like ImageNet-O and ImageNet-C, ProSMIN demonstrates its scalability and real-world applicability.

We consider the task of identifying the Copeland winner(s) in a dueling bandits problem with ternary feedback. This is an underexplored but practically relevant variant of the conventional dueling bandits problem, in which, in addition to strict preference between two arms, one may observe feedback in the form of an indifference. We provide a lower bound on the sample complexity for any learning algorithm finding the Copeland winner(s) with a fixed error probability. Moreover, we propose POCOWISTA, an algorithm with a sample complexity that almost matches this lower bound, and which shows excellent empirical performance, even for the conventional dueling bandits problem. For the case where the preference probabilities satisfy a specific type of stochastic transitivity, we provide a refined version with an improved worst case sample complexity.

Addressing the limitations of individual attribution scores via the Shapley value (SV), the field of explainable AI (XAI) has recently explored intricate interactions of features or data points. In particular, extensions of the SV, such as the Shapley Interaction Index (SII), have been proposed as a measure to still benefit from the axiomatic basis of the SV. However, similar to the SV, their exact computation remains computationally prohibitive. Hence, we propose with SVARM-IQ a sampling-based approach to efficiently approximate Shapley-based interaction indices of any order. SVARM-IQ can be applied to a broad class of interaction indices, including the SII, by leveraging a novel stratified representation. We provide non-asymptotic theoretical guarantees on its approximation quality and empirically demonstrate that SVARM-IQ achieves state-of-the-art estimation results in practical XAI scenarios on different model classes and application domains.

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and epistemic uncertainty based on proper scoring rules, which are loss functions with the meaningful property that they incentivize the learner to predict ground-truth (conditional) probabilities. We assume two common representations of (epistemic) uncertainty, namely, in terms of a credal set, i.e. a set of probability distributions, or a second-order distribution, i.e., a distribution over probability distributions. Our framework establishes a natural bridge between these representations. We provide a formal justification of our approach and introduce new measures of epistemic and aleatoric uncertainty as concrete instantiations.

In today’s data-driven world, the proliferation of publicly available information raises security concerns due to the information leakage (IL) problem. IL involves unintentionally exposing sensitive information to unauthorized parties via observable system information. Conventional statistical approaches rely on estimating mutual information (MI) between observable and secret information for detecting ILs, face challenges of the curse of dimensionality, convergence, computational complexity, and MI misestimation. Though effective, emerging supervised machine learning based approaches to detect ILs are limited to binary system sensitive information and lack a comprehensive framework. To address these limitations, we establish a theoretical framework using statistical learning theory and information theory to quantify and detect IL accurately. Using automated machine learning, we demonstrate that MI can be accurately estimated by approximating the typically unknown Bayes predictor’s log-loss and accuracy. Based on this, we show how MI can effectively be estimated to detect ILs. Our method performs superior to state-of-the-art baselines in an empirical study considering synthetic and real-world OpenSSL TLS server datasets.

The Shapley value, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is due to axiomatic properties that only the Shapley value satisfies, which, however, comes at the expense of an exact computation growing exponentially with the number of agents. Accordingly, a number of works are devoted to the efficient approximation of the Shapley value, most of them revolve around the notion of an agent’s marginal contribution. In this paper, we propose with SVARM and Stratified SVARM two parameter-free and domain-independent approximation algorithms based on a representation of the Shapley value detached from the notion of marginal contribution. We prove unmatched theoretical guarantees regarding their approximation quality and provide empirical results including synthetic games as well as common explainability use cases comparing ourselves with state-of-the-art methods.

Label noise poses an important challenge in machine learning, especially in deep learning, in which large models with high expressive power dominate the field. Models of that kind are prone to memorizing incorrect labels, thereby harming generalization performance. Many methods have been proposed to address this problem, including robust loss functions and more complex label correction approaches. Robust loss functions are appealing due to their simplicity, but typically lack flexibility, while label correction usually adds substantial complexity to the training setup. In this paper, we suggest to address the shortcomings of both methodologies by ‘ambiguating’ the target information, adding additional, complementary candidate labels in case the learner is not sufficiently convinced of the observed training label. More precisely, we leverage the framework of so-called superset learning to construct set-valued targets based on a confidence threshold, which deliver imprecise yet more reliable beliefs about the ground-truth, effectively helping the learner to suppress the memorization effect. In an extensive empirical evaluation, our method demonstrates favorable learning behavior on synthetic and real-world noise, confirming the effectiveness in detecting and correcting erroneous training labels.

While shallow decision trees may be interpretable, larger ensemble models like gradient-boosted trees, which often set the state of the art in machine learning problems involving tabular data, still remain black box models. As a remedy, the Shapley value (SV) is a well-known concept in explainable artificial intelligence (XAI) research for quantifying additive feature attributions of predictions. The model-specific TreeSHAP methodology solves the exponential complexity for retrieving exact SVs from tree-based models. Expanding beyond individual feature attribution, Shapley interactions reveal the impact of intricate feature interactions of any order. In this work, we present TreeSHAP-IQ, an efficient method to compute any-order additive Shapley interactions for predictions of tree-based models. TreeSHAP-IQ is supported by a mathematical framework that exploits polynomial arithmetic to compute the interaction scores in a single recursive traversal of the tree, akin to Linear TreeSHAP. We apply TreeSHAP-IQ on state-of-the-art tree ensembles and explore interactions on well-established benchmark datasets.

Multiple criteria decision aiding (MCDA) and preference learning (PL) are established research fields, which have different roots, developed in different communities – the former in the decision sciences and operations research, the latter in AI and machine learning – and have their own agendas in terms of problem setting, assumptions, and criteria of success. In spite of this, they share the major goal of constructing practically useful decision models that either support humans in the task of choosing the best, classifying, or ranking alternatives from a given set, or even automate decision-making by acting autonomously on behalf of the human. Therefore, MCDA and PL can complement and mutually benefit from each other, a potential that has been exhausted only to some extent so far. By elaborating on the connection between MCDA and PL in more depth, our goal is to stimulate further research at the junction of these two fields. To this end, we first review both methodologies, MCDA in this part of the paper and PL in the second part, with the intention of highlighting their most common elements. In the second part, we then compare both methodologies in a systematic way and give an overview of existing work on combining PL and MCDA.

This article elaborates on the connection between multiple criteria decision aiding (MCDA) and preference learning (PL), two research fields with different roots and developed in different communities. It complements the first part of the paper, in which we started with a review of MCDA. In this part, a similar review will be given for PL, followed by a systematic comparison of both methodologies, as well as an overview of existing work on combining PL and MCDA. Our main goal is to stimulate further research at the junction of these two methodologies.

In today’s data-driven world, the proliferation of publicly available information raises security concerns due to the information leakage (IL) problem. IL involves unintentionally exposing sensitive information to unauthorized parties via observable system information. Conventional statistical approaches rely on estimating mutual information (MI) between observable and secret information for detecting ILs, face challenges of the curse of dimensionality, convergence, computational complexity, and MI misestimation. Though effective, emerging supervised machine learning based approaches to detect ILs are limited to binary system sensitive information and lack a comprehensive framework. To address these limitations, we establish a theoretical framework using statistical learning theory and information theory to quantify and detect IL accurately. Using automated machine learning, we demonstrate that MI can be accurately estimated by approximating the typically unknown Bayes predictor’s log-loss and accuracy. Based on this, we show how MI can effectively be estimated to detect ILs. Our method performs superior to state-of-the-art baselines in an empirical study considering synthetic and real-world OpenSSL TLS server datasets.

Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature interactions. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. Here, we propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for arbitrary cardinal interaction indices (CII), i.e. interaction indices that satisfy the linearity, symmetry and dummy axiom. SHAP-IQ is based on a novel representation and, in contrast to existing methods, we provide theoretical guarantees for its approximation quality, as well as estimates for the variance of the point estimates. For the special case of SV, our approach reveals a novel representation of the SV and corresponds to Unbiased KernelSHAP with a greatly simplified calculation. We illustrate the computational efficiency and effectiveness by explaining language, image classification and high-dimensional synthetic models.

Reinforcement learning from human feedback (RLHF) is a variant of reinforcement learning (RL) that learns from human feedback instead of relying on an engineered reward function. Building on prior work on the related setting of preference-based reinforcement learning (PbRL), it stands at the intersection of artificial intelligence and human-computer interaction. This positioning offers a promising avenue to enhance the performance and adaptability of intelligent systems while also improving the alignment of their objectives with human values. The training of large language models (LLMs) has impressively demonstrated this potential in recent years, where RLHF played a decisive role in directing the model’s capabilities toward human objectives. This article provides a comprehensive overview of the fundamentals of RLHF, exploring the intricate dynamics between RL agents and human input. While recent focus has been on RLHF for LLMs, our survey adopts a broader perspective, examining the diverse applications and wide-ranging impact of the technique. We delve into the core principles that underpin RLHF, shedding light on the symbiotic relationship between algorithms and human feedback, and discuss the main research trends in the field. By synthesizing the current landscape of RLHF research, this article aims to provide researchers as well as practitioners with a comprehensive understanding of this rapidly growing field of research.

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way to use variance-based measures to quantify uncertainty on the basis of second-order distributions in classification problems. A distinctive feature of the measures is the ability to reason about uncertainties on a class-based level, which is useful in situations where nuanced decision-making is required. Recalling some properties from the literature, we highlight that the variance-based measures satisfy important (axiomatic) properties. In addition to this axiomatic approach, we present empirical results showing the measures to be effective and competitive to commonly used entropy-based measures.

A scoring system is a simple decision model that checks a set of features, adds a certain number of points to a total score for each feature that is satisfied, and finally makes a decision by comparing the total score to a threshold. Scoring systems have a long history of active use in safety-critical domains such as healthcare and justice, where they provide guidance for making objective and accurate decisions. Given their genuine interpretability, the idea of learning scoring systems from data is obviously appealing from the perspective of explainable AI. In this paper, we propose a practically motivated extension of scoring systems called probabilistic scoring lists (PSL), as well as a method for learning PSLs from data. Instead of making a deterministic decision, a PSL represents uncertainty in the form of probability distributions. Moreover, in the spirit of decision lists, a PSL evaluates features one by one and stops as soon as a decision can be made with enough confidence. To evaluate our approach, we conduct a case study in the medical domain.

Realtime algorithm configuration is concerned with the task of designing a dynamic algorithm configurator that observes sequentially arriving problem instances of an algorithmic problem class for which it selects suitable algorithm configurations (e.g., minimal runtime) of a specific target algorithm. The Contextual Preselection under the Plackett-Luce (CPPL) algorithm maintains a pool of configurations from which a set of algorithm configurations is selected that are run in parallel on the current problem instance. It uses the well-known UCB selection strategy from the bandit literature, while the pool of configurations is updated over time via a racing mechanism. In this paper, we investigate whether the performance of CPPL can be further improved by using different bandit-based selection strategies as well as a ranking-based strategy to update the candidate pool. Our experimental results show that replacing these components can indeed improve performance again significantly.

The selection of useful, informative, and meaningful features is a key prerequisite for the successful application of machine learning in practice, especially in knowledge-intense domains like decision support. Here, the task of feature selection, or ranking features by importance, can, in principle, be solved automatically in a data-driven way but also supported by expert knowledge. Besides, one may of course, conceive a combined approach, in which a learning algorithm closely interacts with a human expert. In any case, finding an optimal approach requires a basic understanding of human capabilities in judging the importance of features compared to those of a learning algorithm. Hereto, we conducted a case study in the medical domain, comparing feature rankings based on human judgment to rankings automatically derived from data. The quality of a ranking is determined by the performance of a decision list processing features in the order specified by the ranking, more specifically by so-called probabilistic scoring systems.

This paper proposes a novel approach for modeling observational data in the form of expert ratings, which are commonly given on an ordered (numerical or ordinal) scale. In practice, such ratings are often biased, due to the expert’s preferences, psychological effects, etc. Our approach aims to rectify these biases, thereby preventing machine learning methods from transferring them to models trained on the data. To this end, we make use of so-called label smoothing, which allows for redistributing probability mass from the originally observed rating to other ratings, which are considered as possible corrections. This enables the incorporation of domain knowledge into the standard cross-entropy loss and leads to flexibly configurable models. Concretely, our method is realized for ordinal ratings and allows for arbitrary unimodal smoothings using a binary smoothing relation. Additionally, the paper suggests two practically motivated smoothing heuristics to address common biases in observational data, a time-based smoothing to handle concept drift and a class-wise smoothing based on class priors to mitigate data imbalance. The effectiveness of the proposed methods is demonstrated on four real-world goodwill assessment data sets of a car manufacturer with the aim of automating goodwill decisions. Overall, this paper presents a promising approach for modeling ordinal observational data that can improve decision-making processes and reduce reliance on human expertise.

Existing methods for explainable artificial intelligence (XAI), including popular feature importance measures such as SAGE, are mostly restricted to the batch learning scenario. However, machine learning is often applied in dynamic environments, where data arrives continuously and learning must be done in an online manner. Therefore, we propose iSAGE, a time- and memory-efficient incrementalization of SAGE, which is able to react to changes in the model as well as to drift in the data-generating process. We further provide efficient feature removal methods that break (interventional) and retain (observational) feature dependencies. Moreover, we formally analyze our explanation method to show that iSAGE adheres to similar theoretical properties as SAGE. Finally, we evaluate our approach in a thorough experimental analysis based on well-established data sets and data streams with concept drift.

While the predictions produced by conformal prediction are set-valued, the data used for training and calibration is supposed to be precise. In the setting of superset learning or learning from partial labels, a variant of weakly supervised learning, it is exactly the other way around: training data is possibly imprecise (set-valued), but the model induced from this data yields precise predictions. In this paper, we combine the two settings by making conformal prediction amenable to set-valued training data. We propose a generalization of the conformal prediction procedure that can be applied to set-valued training and calibration data. We prove the validity of the proposed method and present experimental studies in which it compares favorably to natural baselines.

In their seminal 1990 paper, Wasserman and Kadane establish an upper bound for the Bayes’ posterior probability of a measurable set A, when the prior lies in a class of probability measures and the likelihood is precise. They also give a sufficient condition for such upper bound to hold with equality. In this paper, we introduce a generalization of their result by additionally addressing uncertainty related to the likelihood. We give an upper bound for the posterior probability when both the prior and the likelihood belong to a set of probabilities. Furthermore, we give a sufficient condition for this upper bound to become an equality. This result is interesting on its own, and has the potential of being applied to various fields of engineering (e.g. model predictive control), machine learning, and artificial intelligence.

Measures of rank correlation are commonly used in statistics to capture the degree of concordance between two orderings of the same set of items. Standard measures like Kendall’s tau and Spearman’s rho coefficient put equal emphasis on each position of a ranking. Yet, motivated by applications in which some of the positions (typically those on the top) are more important than others, a few weighted variants of these measures have been proposed. Most of these generalizations fail to meet desirable formal properties, however. Besides, they are often quite inflexible in the sense of committing to a fixed weighing scheme. In this paper, we propose a weighted rank correlation measure on the basis of fuzzy order relations. Our measure, called scaled gamma, is related to Goodman and Kruskal’s gamma rank correlation. It is parametrized by a fuzzy equivalence relation on the rank positions, which in turn is specified conveniently by a so-called scaling function. This approach combines soundness with flexibility: it has a sound formal foundation and allows for weighing rank positions in a flexible way.

Adequate uncertainty representation and quantification have become imperative in various scientific disciplines, especially in machine learning and artificial intelligence. As an alternative to representing uncertainty via one single probability measure, we consider credal sets (convex sets of probability measures). The geometric representation of credal sets as d-dimensional polytopes implies a geometric intuition about (epistemic) uncertainty. In this paper, we show that the volume of the geometric representation of a credal set is a meaningful measure of epistemic uncertainty in the case of binary classification, but less so for multi-class classification. Our theoretical findings highlight the crucial role of specifying and employing uncertainty measures in machine learning in an appropriate way, and for being aware of possible pitfalls.

The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted in information theory, seem appealing at first glance, we identify various incoherencies that call their appropriateness into question. In addition to the measures themselves, we critically discuss the idea of an additive decomposition of total uncertainty into its aleatoric and epistemic constituents. Experiments across different computer vision tasks support our theoretical findings and raise concerns about current practice in uncertainty quantification.

In recent years, Explainable AI (xAI) attracted a lot of attention as various countries turned explanations into a legal right. xAI algorithms enable humans to understand the underlying models and explain their behavior, leading to insights through which the models can be analyzed and improved beyond the accuracy metric by, e.g., debugging the learned pattern and reducing unwanted biases. However, the widespread use of xAI and the rapidly growing body of published research in xAI have brought new challenges. A large number of xAI algorithms can be overwhelming and make it difficult for practitioners to choose the correct xAI algorithm for their specific use case. This problem is further exacerbated by the different approaches used to assess novel xAI algorithms, making it difficult to compare them to existing methods. To address this problem, we introduce Compare-xAI, a benchmark that allows for a direct comparison of popular xAI algorithms with a variety of different use cases. We propose a scoring protocol employing a range of functional tests from the literature, each targeting a specific end-user requirement in explaining a model. To make the benchmark results easily accessible, we group the tests into four categories (fidelity, fragility, stability, and stress tests). We present results for 13 xAI algorithms based on 11 functional tests. After analyzing the findings, we derive potential solutions for data science practitioners as workarounds to the found practical limitations. Finally, Compare-xAI is a tentative to unify systematic evaluation and comparison methods for xAI algorithms with a focus on the end-user’s requirements.

Post-hoc explanation techniques such as the well-established partial dependence plot (PDP), which investigates feature dependencies, are used in explainable artificial intelligence (XAI) to understand black-box machine learning models. While many real-world applications require dynamic models that constantly adapt over time and react to changes in the underlying distribution, XAI, so far, has primarily considered static learning environments, where models are trained in a batch mode and remain unchanged. We thus propose a novel model-agnostic XAI framework called incremental PDP (iPDP) that extends on the PDP to extract time-dependent feature effects in non-stationary learning environments. We formally analyze iPDP and show that it approximates a time-dependent variant of the PDP that properly reacts to real and virtual concept drift. The time-sensitivity of iPDP is controlled by a single smoothing parameter, which directly corresponds to the variance and the approximation error of iPDP in a static learning environment. We illustrate the efficacy of iPDP by showcasing an example application for drift detection and conducting multiple experiments on real-world and synthetic data sets and streams.

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring rules.

In multi-class classification, it can be beneficial to decompose a learning problem into several simpler problems. One such reduction technique is the use of so-called nested dichotomies, which recursively bisect the set of possible classes such that the resulting subsets can be arranged in the form of a binary tree, where each split defines a binary classification problem. Recently, a genetic algorithm for optimizing the structure of such nested dichotomies has achieved state-of-the-art results. Motivated by its success, we propose to extend this approach using a co-evolutionary scheme to optimize both the structure of nested dichotomies and their composition into ensembles through which they are evaluated. Furthermore, we present an experimental study showing this approach to yield ensembles of nested dichotomies at substantially lower cost and, in some cases, even with an improved generalization performance.

Automated machine learning (AutoML) strives for the automatic configuration of machine learning algorithms and their composition into an overall (software) solution — a machine learning pipeline — tailored to the learning task (dataset) at hand. Over the last decade, AutoML has developed into an independent research field with hundreds of contributions. At the same time, AutoML is being criticized for its high resource consumption as many approaches rely on the (costly) evaluation of many machine learning pipelines, as well as the expensive large-scale experiments across many datasets and approaches. In the spirit of recent work on Green AI, this paper proposes Green AutoML, a paradigm to make the whole AutoML process more environmentally friendly. Therefore, we first elaborate on how to quantify the environmental footprint of an AutoML tool. Afterward, different strategies on how to design and benchmark an AutoML tool w.r.t. their “greenness”, i.e., sustainability, are summarized. Finally, we elaborate on how to be transparent about the environmental footprint and what kind of research incentives could direct the community in a more sustainable AutoML research direction. As part of this, we propose a sustainability checklist to be attached to every AutoML paper featuring all core aspects of Green AutoML.

The Go programming language offers strong protection from memory corruption. As an escape hatch of these protections, it provides the unsafe package. Previous studies identified that this unsafe package is frequently used in real-world code for several purposes, e.g., serialization or casting types. Due to the variety of these reasons, it may be possible to refactor specific usages to avoid potential vulnerabilities. However, the classification of unsafe usages is challenging and requires the context of the call and the program’s structure. In this paper, we present the first automated classifier for unsafe usages in Go, UnGoML, to identify what is done with the unsafe package and why it is used. For UnGoML, we built four custom deep learning classifiers trained on a manually labeled data set. We represent Go code as enriched control-flow graphs (CFGs) and solve the label prediction task with one single-vertex and three context-aware classifiers. All three context-aware classifiers achieve a top-1 accuracy of more than 86% for both dimensions, WHAT and WHY. Furthermore, in a set-valued conformal prediction setting, we achieve accuracies of more than 93% with mean label set sizes of 2 for both dimensions. Thus, UnGoML can be used to efficiently filter unsafe usages for use cases such as refactoring or a security audit.

In anomaly detection, a prominent task is to induce a model to identify anomalies learned solely based on normal data. Generally, one is interested in finding an anomaly detector that correctly identifies anomalies, i.e., data points that do not belong to the normal class, without raising too many false alarms. Which anomaly detector is best suited depends on the dataset at hand and thus needs to be tailored. The quality of an anomaly detector may be assessed via confusion-based metrics such as the Matthews correlation coefficient (MCC). However, since during training only normal data is available in a semi-supervised setting, such metrics are not accessible. To facilitate automated machine learning for anomaly detectors, we propose to employ meta-learning to predict MCC scores using the metrics that can be computed with normal data only and order anomaly detectors using the predicted scores for selection. First promising results can be obtained considering the hypervolume and the false positive rate as meta-features.

PyExperimenter is a tool to facilitate the setup, documentation, execution, and subsequent evaluation of results from an empirical study of algorithms and in particular is designed to reduce the involved manual effort significantly. It is intended to be used by researchers in the field of artificial intelligence, but is not limited to those.
The empirical analysis of algorithms is often accompanied by the execution of algorithms for different inputs and variants of the algorithms, specified via parameters, and the measurement of non-functional properties. Since the individual evaluations are usually independent, the evaluation can be performed in a distributed manner on an HPC system. However, setting up, documenting, and evaluating the results of such a study is often file-based. Usually, this requires extensive manual work to create configuration files for the inputs or to read and aggregate measured results from a report file. In addition, monitoring and restarting individual executions is tedious and time-consuming.
PyExperimenter adresses theses challenges by means of a single well defined configuration file and a central database for managing massively parallel evaluations, as well as collecting and aggregating their results. Thereby, PyExperimenter alleviates the aforementioned overhead and allows experiment executions to be defined and monitored with ease.

With the rapid growth of data availability and usage, quantifying the added value of each training data point has become a crucial process in the field of artificial intelligence. The Shapley values have been recognized as an effective method for data valuation, enabling efficient training set summarization, acquisition, and outlier removal. In this paper, we introduce ‘STI-KNN’, an innovative algorithm that calculates the exact pair-interaction Shapley values for KNN models in $O(t n^2)$ time, which is a significant improvement over the $O(2^n)$ time complexity of baseline methods. By using STI-KNN, we can efficiently and accurately evaluate the value of individual data points, leading to improved training outcomes and ultimately enhancing the effectiveness of artificial intelligence applications.

We study the algorithm configuration (AC) problem, in which one seeks to find an optimal parameter configuration of a given target algorithm in an automated way. Although this field of research has experienced much progress recently regarding approaches satisfying strong theoretical guarantees, there is still a gap between the practical performance of these approaches and the heuristic state-of-the-art approaches. Recently, there has been significant progress in designing AC approaches that satisfy strong theoretical guarantees. However, a significant gap still remains between the practical performance of these approaches and state-of-the-art heuristic methods. To this end, we introduce AC-Band, a general approach for the AC problem based on multi-armed bandits that provides theoretical guarantees while exhibiting strong practical performance. We show that AC-Band requires significantly less computation time than other AC approaches providing theoretical guarantees while still yielding high-quality configurations.

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however, has its own parameters that influence its performance. One of these parameters, the maximal budget, is especially problematic: If chosen too small, the budget needs to be increased in hindsight and, as Hyperband is not incremental by design, the entire algorithm must be re-run. This is not only costly but also comes with a loss of valuable knowledge already accumulated. In this paper, we propose incremental variants of Hyperband that eliminate these drawbacks, and show that these variants satisfy theoretical guarantees qualitatively similar to those for the original Hyperband with the ‘right’ budget. Moreover, we demonstrate their practical utility in experiments with benchmark data sets.

We consider a resource-aware variant of the classical multi-armed bandit problem: In each round, the learner selects an arm and determines a resource limit. It then observes a corresponding (random) reward, provided the (random) amount of consumed resources remains below the limit. Otherwise, the observation is censored, i.e., no reward is obtained. For this problem setting, we introduce a measure of regret, which incorporates both the actual amount of consumed resources of each learning round and the optimality of realizable rewards as well as the risk of exceeding the allocated resource limit. Thus, to minimize regret, the learner needs to set a resource limit and choose an arm in such a way that the chance to realize a high reward within the predefined resource limit is high, while the resource limit itself should be kept as low as possible. We propose a UCB-inspired online learning algorithm, which we analyze theoretically in terms of its regret upper bound. In a simulation study, we show that our learning algorithm outperforms straightforward extensions of standard multi-armed bandit algorithms.

The usage of convolutional neural networks (CNNs) to break cryptographic systems through hardware side-channels has enabled fast and adaptable attacks on devices like smart cards and TPMs. Current literature proposes fixed CNN architectures designed by domain experts to break such systems, which is time-consuming and unsuitable for attacking a new system. Recently, an approach using neural architecture search (NAS), which is able to acquire a suitable architecture automatically, has been explored. These works use the secret key information in the attack dataset for optimization and only explore two different search strategies using one-dimensional CNNs. We propose a NAS approach that relies only on using the profiling dataset for optimization, making it fully black-box. Using a large-scale experimental parameter study, we explore which choices for NAS, such as 1-D or 2-D CNNs and search strategy, produce the best results on 10 state-of-the-art datasets for Hamming weight and identity leakage models. We show that applying the random search strategy on 1-D inputs results in a high success rate and retrieves the correct secret key using a single attack trace on two of the datasets. This combination matches the attack efficiency of fixed CNN architectures, outperforming them in 4 out of 10 datasets. Our experiments also point toward the need for repeated attack evaluations of machine learning-based solutions in order to avoid biased performance estimates.

Errors and inaccuracies in the representation of clouds in convection-permitting numerical weather prediction models can be caused by various sources, including the forcing and boundary conditions, the representation of orography, and the accuracy of the numerical schemes determining the evolution of humidity and temperature. Moreover, the parametrization of microphysics and the parametrization of processes in the surface and boundary layers do have a significant influence. These schemes typically contain several tunable parameters that are either non-physical or only crudely known, leading to model errors and imprecision. Furthermore, not accounting for uncertainties in these parameters might lead to overconfidence in the model during forecasting and data assimilation (DA).
Traditionally, the numerical values of model parameters are chosen by manual model tuning. More objectively, they can be estimated from observations by the so-called augmented state approach during the data assimilation [7]. Alternatively, the problem of estimating model parameters has recently been tackled by means of a hybrid approach combining DA with machine learning, more specifically a Bayesian neural network (BNN) [6]. As a proof of concept, this approach has been applied to a one-dimensional modified shallow-water (MSW) model [8].
Even though the BNN is able to accurately estimate the model parameters and their uncertainties, its high computational cost poses an obstacle to its use in operational settings where the grid sizes of the atmospheric fields are much larger than in the simple MSW model. Because random forests (RF) [2] are typically computationally cheaper while still being able to adequately represent uncertainties, we are interested in comparing RFs and BNNs. To this end, we follow [6] and again consider the problem of estimating the three model parameters of the MSW model as a function of the atmospheric state.

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner’s (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.

We consider the combinatorial bandits problem with semi-bandit feedback under finite sampling budget constraints, in which the learner can carry out its action only for a limited number of times specified by an overall budget. The action is to choose a set of arms, whereupon feedback for each arm in the chosen set is received. Unlike existing works, we study this problem in a non-stochastic setting with subset-dependent feedback, i.e., the semi-bandit feedback received could be generated by an oblivious adversary and also might depend on the chosen set of arms. In addition, we consider a general feedback scenario covering both the numerical-based as well as preference-based case and introduce a sound theoretical framework for this setting guaranteeing sensible notions of optimal arms, which a learner seeks to find. We suggest a generic algorithm suitable to cover the full spectrum of conceivable arm elimination strategies from aggressive to conservative. Theoretical questions about the sufficient and necessary budget of the algorithm to find the best arm are answered and complemented by deriving lower bounds for any learning algorithm for this problem scenario.

In this article we introduce and describe SCIKIT-WEAK, a Python library inspired by SCIKIT-LEARN and developed to provide an easy-to-use framework for dealing with weakly supervised and imprecise data learning problems, which, despite their importance in real-world settings, cannot be easily managed by existing libraries. We provide a rationale for the development of such a library, then we discuss its design and the currently implemented methods and classes, which encompass several state-of-the-art algorithms.

Algorithm configuration (AC) is concerned with the automated search of the most suitable parameter configuration of a parametrized algorithm. There is currently a wide variety of AC problem variants and methods proposed in the literature. Existing reviews do not take into account all derivatives of the AC problem, nor do they offer a complete classification scheme. To this end, we introduce taxonomies to describe the AC problem and features of configuration methods, respectively. We review existing AC literature within the lens of our taxonomies, outline relevant design choices of configuration approaches, contrast methods and problem variants against each other, and describe the state of AC in industry. Finally, our review provides researchers and practitioners with a look at future research directions in the field of AC.

Algorithm configuration (AC) is concerned with the automated search of the most suitable parameter configuration of a parametrized algorithm. There is currently a wide variety of AC problem variants and methods proposed in the literature. Existing reviews do not take into account all derivatives of the AC problem, nor do they offer a complete classification scheme. To this end, we introduce taxonomies to describe the AC problem and features of configuration methods, respectively. We review existing AC literature within the lens of our taxonomies, outline relevant design choices of configuration approaches, contrast methods and problem variants against each other, and describe the state of AC in industry. Finally, our review provides researchers and practitioners with a look at future research directions in the field of AC.

Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for which its current prediction is maximally uncertain. The predictions as well as the measures used to quantify the degree of uncertainty, such as entropy, are traditionally of a probabilistic nature. Yet, alternative approaches to capturing uncertainty in machine learning, alongside with corresponding uncertainty measures, have been proposed in recent years. In particular, some of these measures seek to distinguish different sources and to separate different types of uncertainty, such as the reducible (epistemic) and the irreducible (aleatoric) part of the total uncertainty in a prediction. The goal of this paper is to elaborate on the usefulness of such measures for uncertainty sampling, and to compare their performance in active learning. To this end, we instantiate uncertainty sampling with different measures, analyze the properties of the sampling strategies thus obtained, and compare them in an experimental study.