arXiv:2511.15146v1 Announce Type: new 
Abstract: Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. A candidate output is included in the prediction set if its non-conformity score is not considered extreme relative to the scores observed on a set of calibration examples. However, this procedure is only straightforward when scores are scalar-valued, which has limited CP to real-valued scores or ad-hoc reductions to one dimension. The problem of ordering vectors has been studied via optimal transport (OT), which provides a principled method for defining vector-ranks and multivariate quantile regions, though typically with only asymptotic coverage guarantees. We restore finite-sample, distribution-free coverage by conformalizing the vector-valued OT quantile region. Here, a candidate's rank is defined via a transport map computed for the calibration scores augmented with that candidate's score. This defines a continuum of OT problems for which we prove that the resulting optimal assignment is piecewise-constant across a fixed polyhedral partition of the score space. This allows us to characterize the entire prediction set tractably, and provides the machinery to address a deeper limitation of prediction sets: that they only indicate which outcomes are plausible, but not their relative likelihood. In one dimension, conformal predictive distributions (CPDs) fill this gap by producing a predictive distribution with finite-sample calibration. Extending CPDs beyond one dimension remained an open problem. We construct, to our knowledge, the first multivariate CPDs with finite-sample calibration, i.e., they define a valid multivariate distribution where any derived uncertainty region automatically has guaranteed coverage. We present both conservative and exact randomized versions, the latter resulting in a multivariate generalization of the classical Dempster-Hill procedure.

يتناول المقال التقدم في التنبؤ المتوافق (CP) من خلال الاستفادة من النقل الأمثل (OT) لتوسيع CP إلى إعدادات متعددة المتغيرات. تقتصر طرق CP التقليدية على الدرجات العددية، لكن هذه الطريقة الجديدة تسمح بالدرجات المتجهة، مما يعزز دقة قياس عدم اليقين في مخرجات النموذج. تستعيد الطريقة المقترحة ضمانات التغطية لعينة محدودة، مما يمثل تحسينًا كبيرًا في مجال التعلم الآلي.

El artículo discute los avances en la predicción conformal (CP) aprovechando el transporte óptimo (OT) para extender la CP a configuraciones multivariadas. Los métodos tradicionales de CP están limitados a puntuaciones escalares, pero este nuevo enfoque permite puntuaciones vectoriales, mejorando la precisión de la cuantificación de la incertidumbre en las salidas del modelo. El método propuesto restaura las garantías de cobertura de muestra finita, lo que representa una mejora significativa en el campo del aprendizaje automático.

L'article aborde les avancées dans la prédiction conforme (CP) en utilisant le transport optimal (OT) pour étendre la CP à des contextes multivariés. Les méthodes CP traditionnelles sont limitées aux scores scalaires, mais cette nouvelle approche permet des scores vectoriels, améliorant ainsi la précision de la quantification de l'incertitude dans les résultats des modèles. La méthode proposée restaure les garanties de couverture à échantillon fini, représentant une amélioration significative dans le domaine de l'apprentissage automatique.

The article discusses advancements in conformal prediction (CP) by leveraging optimal transport (OT) to extend CP to multivariate settings. Traditional CP methods are limited to scalar scores, but this new approach allows for vector-valued scores, enhancing the accuracy of uncertainty quantification in model outputs. The proposed method restores finite-sample coverage guarantees, making it a significant improvement in the field of machine learning.

Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distribution to Multivariate Settings

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