mlsanityData to 14 Oct 2026

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

arXiv 2306.12803 ↗First posted 22 Jun 2023stat.ML cs.LG math.STcited by 13

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Abstract (arXiv)

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.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Builds on 13 of its 80 references that are in the map. First posted on arXiv 22 Jun 2023.

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13 of 80 references.

References · 13

  1. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 913
  2. 2018Predictive Uncertainty Estimation via Prior Networkscited by 557
  3. 2022Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisationcited by 66
  4. 2022Statistical Comparisons of Classifiers by Generalized Stochastic Dominancecited by 20
  5. 2021Ensemble-based Uncertainty Quantification: Bayesian versus Credal Inferencecited by 16
  6. 2021Credal Self-Supervised Learningcited by 15
  7. 2016Statistical comparison of classifiers through Bayesian hierarchical modellingcited by 14
  8. 2021Accounting for Gaussian Process Imprecision in Bayesian Optimizationcited by 13
  9. 2021Information efficient learning of complexly structured preferences: Elicitation procedures and their application to decision making under uncertaintycited by 10
  10. 2022Attention-based Random Forest and Contamination Modelcited by 10
  11. 2022Multi-Target Decision Making under Conditions of Severe Uncertaintycited by 7
  12. 2022Learning to Optimize with Stochastic Dominance Constraintscited by 5
1 more
  1. 2023Depth Functions for Partial Orders with a Descriptive Analysis of Machine Learning Algorithmscited by 5

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Citing papers per year: 2023: 1; 2024: 7; 2025: 4; 2026: 1.

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  1. 2024Explaining Bayesian Optimization by Shapley Values Facilitates Human-AI Collaborationcited by 12
  2. 2024Statistical Multicriteria Benchmarking via the GSD-Frontcited by 11
  3. 2024Towards Better Open-Ended Text Generation: A Multicriteria Evaluation Frameworkcited by 9
  4. 2025Statistical Multicriteria Evaluation of LLM-Generated Textcited by 9
  5. 2024Partial Rankings of Optimizerscited by 8
  6. 2024Semi-Supervised Learning guided by the Generalized Bayes Rule under Soft Revisioncited by 6
  7. 2025A Statistical Case Against Empirical Human-AI Alignmentcited by 6
  8. 2025Generalization Bounds and Stopping Rules for Learning with Self-Selected Datacited by 5
  9. 2023Pseudo Label Selection is a Decision Problemcited by 4
  10. 2024Towards Bayesian Data Selectioncited by 2
  11. 2024Reciprocal Learningcited by 0
  12. 2025Empirical Decision Theorycited by 0
1 more
  1. 2026Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantificationcited by 0