arXiv:2510.21273v2 Announce Type: replace 
Abstract: Probabilistic models must be well calibrated to support reliable decision-making. While calibration in single-output regression is well studied, defining and achieving multivariate calibration in multi-output regression remains considerably more challenging. The existing literature on multivariate calibration primarily focuses on diagnostic tools based on pre-rank functions, which are projections that reduce multivariate prediction-observation pairs to univariate summaries to detect specific types of miscalibration. In this work, we go beyond diagnostics and introduce a general regularization framework to enforce multivariate calibration during training for arbitrary pre-rank functions. This framework encompasses existing approaches such as highest density region calibration and copula calibration. Our method enforces calibration by penalizing deviations of the projected probability integral transforms (PITs) from the uniform distribution, and can be added as a regularization term to the loss function of any probabilistic predictor. Specifically, we propose a regularization loss that jointly enforces both marginal and multivariate pre-rank calibration. We also introduce a new PCA-based pre-rank that captures calibration along directions of maximal variance in the predictive distribution, while also enabling dimensionality reduction. Across 18 real-world multi-output regression datasets, we show that unregularized models are consistently miscalibrated, and that our methods significantly improve calibration across all pre-rank functions without sacrificing predictive accuracy.

تسلط دراسة جديدة حول الانحدار الاحتمالي متعدد المخرجات الضوء على أهمية المعايرة من أجل اتخاذ قرارات موثوقة. بينما تم بحث المعايرة في المخرجات الفردية بشكل موسع، يتناول هذا المقال تعقيدات تحقيق المعايرة المتعددة المتغيرات، وهو أمر حاسم للتنبؤات الدقيقة في مجالات متنوعة. من خلال التركيز على تنظيم ما قبل الترتيب، يقدم المؤلفون رؤى يمكن أن تعزز فعالية النماذج الاحتمالية، مما يجعل هذا البحث ذا أهمية لكل من الأكاديميين والممارسين في اتخاذ القرارات المعتمدة على البيانات.

Un nuevo estudio sobre la regresión probabilística de múltiples salidas destaca la importancia de la calibración para una toma de decisiones confiable. Mientras que la calibración en salidas únicas ha sido ampliamente investigada, este artículo aborda las complejidades de lograr la calibración multivariada, que es crucial para predicciones precisas en diversos campos. Al centrarse en la regularización previa al rango, los autores proporcionan ideas que podrían mejorar la efectividad de los modelos probabilísticos, haciendo que esta investigación sea significativa tanto para académicos como para profesionales en la toma de decisiones impulsadas por datos.

Une nouvelle étude sur la régression probabiliste multi-sortie souligne l'importance de la calibration pour une prise de décision fiable. Alors que la calibration à sortie unique a été largement étudiée, cet article aborde les complexités de l'atteinte de la calibration multivariée, essentielle pour des prédictions précises dans divers domaines. En se concentrant sur la régularisation pré-rang, les auteurs offrent des perspectives qui pourraient améliorer l'efficacité des modèles probabilistes, rendant cette recherche significative pour les universitaires et les praticiens dans la prise de décision basée sur les données.

A new study on multi-output probabilistic regression highlights the importance of calibration for reliable decision-making. While single-output calibration has been extensively researched, this paper addresses the complexities of achieving multivariate calibration, which is crucial for accurate predictions in various fields. By focusing on pre-rank regularization, the authors provide insights that could enhance the effectiveness of probabilistic models, making this research significant for both academics and practitioners in data-driven decision-making.

Enforcing Calibration in Multi-Output Probabilistic Regression with Pre-rank Regularization

arXiv:2511.18562v1 Announce Type: new 
Abstract: Conformal prediction (CP) provides distribution-free, finite-sample coverage guarantees but critically relies on exchangeability, a condition often violated under distribution shift. We study the robustness of split conformal prediction under adversarial perturbations at test time, focusing on both coverage validity and the resulting prediction set size. Our theoretical analysis characterizes how the strength of adversarial perturbations during calibration affects coverage guarantees under adversarial test conditions. We further examine the impact of adversarial training at the model-training stage. Extensive experiments support our theory: (i) Prediction coverage varies monotonically with the calibration-time attack strength, enabling the use of nonzero calibration-time attack to predictably control coverage under adversarial tests; (ii) target coverage can hold over a range of test-time attacks: with a suitable calibration attack, coverage stays within any chosen tolerance band across a contiguous set of perturbation levels; and (iii) adversarial training at the training stage produces tighter prediction sets that retain high informativeness.

تدرس دراسة حديثة قوة التنبؤ المتوافق المنقسم تحت الهجمات العدائية، مع تسليط الضوء على الاعتماد على التبادل وتأثير الاضطرابات العدائية على صلاحية التغطية وحجم مجموعة التنبؤ. تكشف التحليلات كيف تؤثر قوة الهجوم في وقت المعايرة على ضمانات التغطية أثناء الاختبارات العدائية.

Un estudio reciente investiga la robustez de la predicción conformal dividida bajo ataques adversariales, destacando la dependencia de la intercambiabilidad y el impacto de las perturbaciones adversariales en la validez de la cobertura y el tamaño del conjunto de predicción. El análisis revela cómo la fuerza del ataque en el momento de la calibración influye en las garantías de cobertura durante las pruebas adversariales.

Une étude récente examine la robustesse de la prédiction conforme fractionnée face aux attaques adversariales, mettant en évidence la dépendance à l'échangeabilité et l'impact des perturbations adversariales sur la validité de la couverture et la taille de l'ensemble de prédiction. L'analyse révèle comment la force de l'attaque au moment de la calibration influence les garanties de couverture lors des tests adversariaux.

A recent study investigates the robustness of split conformal prediction under adversarial attacks, highlighting the reliance on exchangeability and the impact of adversarial perturbations on coverage validity and prediction set size. The analysis reveals how calibration-time attack strength influences coverage guarantees during adversarial testing.

Enforcing Calibration in Multi-Output Probabilistic Regression with Pre-rank Regularization

Was this article worth reading? Share it

Spicy Ranks AI

Octofy

Keywords AI