arXiv subjects

Christoph Jansen

Publications and source records attributed to Christoph Jansen.

At least 19 recordsLinked to original sources

arXiv2026

How Hard is it to Rig a Benchmark? A Social Choice Analysis of Leaderboard Robustness

Multi-task benchmarks have become a central pillar of machine learning research, yet their growing influence has incentivised benchmark gaming -- strategic actions taken to improve the leaderboard rank of a specific model. Treating datasets as voters and models as candidates, we consider benchmark-specific training -- the inclusion of benchmark data in training -- as a form of election manipulation. For any ordinal benchmark, the problem of choosing datasets to train on so that a target model becomes top-ranked corresponds to shift bribery, a class of manipulation problems from computational social choice. Leveraging this identification, we show that the benchmark-specific training problem is NP-hard under Borda count and mean win rate. Complementing this worst-case perspective, we introduce the instance-level robustness, the minimum number of datasets a model developer must include in training to top a given leaderboard, and derive expressions for it under arithmetic mean, median, mean win rate and pairwise majority. We evaluate these expressions on MMLU under HELM and on BIG-Bench Hard (BBH) under the Open LLM Leaderboard. Across both suites, mean win rate is hardest to manipulate: this gap is clear on BBH (24 tasks, 4507 models), where its median robustness is 22 tasks (92%), compared with 13 (54%) under arithmetic mean and 12 (50%) under median and pairwise majority.

cs.LG↗

arXiv2026

Robust Bayes Acts under Prior Perturbations: Contamination, Stability, and Selection Paths

This paper develops a quantitative framework to assess the robustness of Bayes-optimal decisions in finite decision problems under model uncertainty. We introduce two complementary stability notions for acts: the robustness radius, measuring the largest perturbation of a reference prior under which an act remains Bayes-optimal, and the contamination need, quantifying the minimal perturbation required for an act to become Bayes-optimal under some nearby prior. Both concepts are characterized via linear programming formulations and computed efficiently using bisection methods exploiting monotonicity properties. Building on these stability measures, we propose a cost-adjusted stability criterion that integrates robustness considerations with act-specific selection costs, yielding a parametric family of decision rules indexed by a regularization parameter. We analyze how optimal act selection evolves along this parameter and derive selection paths that reveal structural transitions between stability-driven and cost-driven regimes. The framework is applied to a portfolio choice problem under uncertainty between different economic regimes. Concretely, using data on historical ETF returns, we compute robustness and contamination profiles for six portfolio strategies and analyze their behavior under heterogeneous belief specifications. The results illustrate that robustness-based selection refines classical expected utility by accounting for prior misspecification.

stat.ME↗

arXiv2026

Beyond Arrow: From Impossibility to Possibilities in Multi-Criteria Benchmarking

Modern benchmarks such as HELM MMLU account for multiple metrics like accuracy, robustness and efficiency. When trying to turn these metrics into a single ranking, natural aggregation procedures can become incoherent or unstable to changes in the model set. We formalize this aggregation as a social choice problem where each metric induces a preference ranking over models on each dataset, and a benchmark operator aggregates these votes across metrics. While prior work has focused on Arrow's impossibility result, we argue that the impossibility often originates from pathological examples and identify sufficient conditions under which these disappear, and meaningful multi-criteria benchmarking becomes possible. In particular, we deal with three restrictions on the combinations of rankings and prove that on single-peaked, group-separable and distance-restricted preferences, the benchmark operator allows for the construction of well-behaved rankings of the involved models. Empirically, we investigate several modern benchmark suites like HELM MMLU and verify which structural conditions are fulfilled on which benchmark problems.

cs.LG↗

arXiv2025

Empirical Decision Theory

Analyzing decision problems under uncertainty commonly relies on idealizing assumptions about the describability of the world, with the most prominent examples being the closed world and the small world assumption. Most assumptions are operationalized by introducing states of the world, conditional on which the decision situation can be analyzed without any remaining uncertainty. Conversely, most classical decision-theoretic approaches are not applicable if the states of the world are inaccessible. We propose a decision model that retains the appeal and simplicity of the original theory, but completely overcomes the need to specify the states of the world explicitly. The main idea of our approach is to address decision problems in a radically empirical way: instead of specifying states and consequences prior to the decision analysis, we only assume a protocol of observed act--consequence pairs as model primitives. We show how optimality in such empirical decision problems can be addressed by using protocol-based empirical choice functions and discuss three approaches for deriving inferential guarantees: (I) consistent statistical estimation of choice sets, (II) consistent statistical testing of choice functions with robustness guarantees, and (III) direct inference for empirical choice functions using credal sets. We illustrate our theory with a proof-of-concept application comparing different prompting strategies in generative AI models.

stat.ME↗

arXiv2025

Statistical Multicriteria Evaluation of LLM-Generated Text

Assessing the quality of LLM-generated text remains a fundamental challenge in natural language processing. Current evaluation approaches often rely on isolated metrics or simplistic aggregations that fail to capture the nuanced trade-offs between coherence, diversity, fluency, and other relevant indicators of text quality. In this work, we adapt a recently proposed framework for statistical inference based on Generalized Stochastic Dominance (GSD) that addresses three critical limitations in existing benchmarking methodologies: the inadequacy of single-metric evaluation, the incompatibility between cardinal automatic metrics and ordinal human judgments, and the lack of inferential statistical guarantees. The GSD-front approach enables simultaneous evaluation across multiple quality dimensions while respecting their different measurement scales, building upon partial orders of decoding strategies, thus avoiding arbitrary weighting of the involved metrics. By applying this framework to evaluate common decoding strategies against human-generated text, we demonstrate its ability to identify statistically significant performance differences while accounting for potential deviations from the i.i.d. assumption of the sampling design.

cs.CL↗

arXiv2025

Consensus in Motion: A Case of Dynamic Rationality of Sequential Learning in Probability Aggregation

We propose a framework for probability aggregation based on propositional probability logic. Unlike conventional judgment aggregation, which focuses on static rationality, our model addresses dynamic rationality by ensuring that collective beliefs update consistently with new information. We show that any consensus-compatible and independent aggregation rule on a non-nested agenda is necessarily linear. Furthermore, we provide sufficient conditions for a fair learning process, where individuals initially agree on a specified subset of propositions known as the common ground, and new information is restricted to this shared foundation. This guarantees that updating individual judgments via Bayesian conditioning-whether performed before or after aggregation-yields the same collective belief. A distinctive feature of our framework is its treatment of sequential decision-making, which allows new information to be incorporated progressively through multiple stages while maintaining the established common ground. We illustrate our findings with a running example in a political scenario concerning healthcare and immigration policies.

cs.AI↗

arXiv2025

A Statistical Case Against Empirical Human-AI Alignment

Empirical human-AI alignment aims to make AI systems act in line with observed human behavior. While noble in its goals, we argue that empirical alignment can inadvertently introduce statistical biases that warrant caution. This position paper thus advocates against naive empirical alignment, offering prescriptive alignment and a posteriori empirical alignment as alternatives. We substantiate our principled argument by tangible examples like human-centric decoding of language models.

cs.AI↗

arXiv2025

Contributions to the Decision Theoretic Foundations of Machine Learning and Robust Statistics under Weakly Structured Information

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.

stat.ML↗

arXiv2024

Reciprocal Learning

We demonstrate that a wide array of machine learning algorithms are specific instances of one single paradigm: reciprocal learning. These instances range from active learning over multi-armed bandits to self-training. We show that all these algorithms do not only learn parameters from data but also vice versa: They iteratively alter training data in a way that depends on the current model fit. We introduce reciprocal learning as a generalization of these algorithms using the language of decision theory. This allows us to study under what conditions they converge. The key is to guarantee that reciprocal learning contracts such that the Banach fixed-point theorem applies. In this way, we find that reciprocal learning algorithms converge at linear rates to an approximately optimal model under relatively mild assumptions on the loss function, if their predictions are probabilistic and the sample adaption is both non-greedy and either randomized or regularized. We interpret these findings and provide corollaries that relate them to specific active learning, self-training, and bandit algorithms.

stat.ML↗

arXiv2024

Statistical Multicriteria Benchmarking via the GSD-Front

Given the vast number of classifiers that have been (and continue to be) proposed, reliable methods for comparing them are becoming increasingly important. The desire for reliability is broken down into three main aspects: (1) Comparisons should allow for different quality metrics simultaneously. (2) Comparisons should take into account the statistical uncertainty induced by the choice of benchmark suite. (3) The robustness of the comparisons under small deviations in the underlying assumptions should be verifiable. To address (1), we propose to compare classifiers using a generalized stochastic dominance ordering (GSD) and present the GSD-front as an information-efficient alternative to the classical Pareto-front. For (2), we propose a consistent statistical estimator for the GSD-front and construct a statistical test for whether a (potentially new) classifier lies in the GSD-front of a set of state-of-the-art classifiers. For (3), we relax our proposed test using techniques from robust statistics and imprecise probabilities. We illustrate our concepts on the benchmark suite PMLB and on the platform OpenML.

stat.ML↗

arXiv2024

Semi-Supervised Learning guided by the Generalized Bayes Rule under Soft Revision

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.

stat.ML↗

arXiv2024

Joining Forces for Pathology Diagnostics with AI Assistance: The EMPAIA Initiative

Over the past decade, artificial intelligence (AI) methods in pathology have advanced substantially. However, integration into routine clinical practice has been slow due to numerous challenges, including technical and regulatory hurdles in translating research results into clinical diagnostic products and the lack of standardized interfaces. The open and vendor-neutral EMPAIA initiative addresses these challenges. Here, we provide an overview of EMPAIA's achievements and lessons learned. EMPAIA integrates various stakeholders of the pathology AI ecosystem, i.e., pathologists, computer scientists, and industry. In close collaboration, we developed technical interoperability standards, recommendations for AI testing and product development, and explainability methods. We implemented the modular and open-source EMPAIA platform and successfully integrated 14 AI-based image analysis apps from 8 different vendors, demonstrating how different apps can use a single standardized interface. We prioritized requirements and evaluated the use of AI in real clinical settings with 14 different pathology laboratories in Europe and Asia. In addition to technical developments, we created a forum for all stakeholders to share information and experiences on digital pathology and AI. Commercial, clinical, and academic stakeholders can now adopt EMPAIA's common open-source interfaces, providing a unique opportunity for large-scale standardization and streamlining of processes. Further efforts are needed to effectively and broadly establish AI assistance in routine laboratory use. To this end, a sustainable infrastructure, the non-profit association EMPAIA International, has been established to continue standardization and support broad implementation and advocacy for an AI-assisted digital pathology future.

cs.CY↗

arXiv2024

Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement

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.

stat.ML↗

arXiv2024

Comparing Machine Learning Algorithms by Union-Free Generic Depth

We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies 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 provide two examples of classifier comparisons on samples of standard benchmark data sets. Our results demonstrate promisingly the wide variety of different analysis approaches based on ufg methods. Furthermore, the examples outline that our approach differs substantially from existing benchmarking approaches, and thus adds a new perspective to the vivid debate on classifier comparison.

cs.LG↗

arXiv2024

Depth Functions for Partial Orders with a Descriptive Analysis of Machine Learning Algorithms

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.

cs.LG↗

arXiv2023

Statistical Comparisons of Classifiers by Generalized Stochastic Dominance

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.

stat.ML↗

arXiv2023

In all LikelihoodS: How to Reliably Select Pseudo-Labeled Data for Self-Training in Semi-Supervised Learning

Self-training is a simple yet effective method within semi-supervised learning. The idea is to iteratively enhance training data by adding pseudo-labeled data. Its generalization performance heavily depends on the selection of these pseudo-labeled data (PLS). In this paper, we aim at rendering PLS more robust towards the involved modeling assumptions. To this end, we propose to select pseudo-labeled data that maximize a multi-objective utility function. The latter is constructed to account for different sources of uncertainty, three of which we discuss in more detail: model selection, accumulation of errors and covariate shift. In the absence of second-order information on such uncertainties, we furthermore consider the generic approach of the generalized Bayesian alpha-cut updating rule for credal sets. As a practical proof of concept, we spotlight the application of three of our robust extensions on simulated and real-world data. Results suggest that in particular robustness w.r.t. model choice can lead to substantial accuracy gains.

stat.ML↗

arXiv2022

Multi-Target Decision Making under Conditions of Severe Uncertainty

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.

cs.AI↗