Multidimensional Uncertainty Quantification via Optimal Transport

• URL: http://arxiv.org/abs/2509.22380v1
• Date: Fri, 26 Sep 2025 14:09:03 GMT
• Title: Multidimensional Uncertainty Quantification via Optimal Transport
• Authors: Nikita Kotelevskii, Maiya Goloburda, Vladimir Kondratyev, Alexander Fishkov, Mohsen Guizani, Eric Moulines, Maxim Panov,
• Abstract summary: We take a multidimensional view on uncertainty quantification (UQ) by stacking complementary UQ measures into a vector.<n>VecUQ-OT shows high efficiency even when individual measures fail.
• Score: 87.97146725546502
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Most uncertainty quantification (UQ) approaches provide a single scalar value as a measure of model reliability. However, different uncertainty measures could provide complementary information on the prediction confidence. Even measures targeting the same type of uncertainty (e.g., ensemble-based and density-based measures of epistemic uncertainty) may capture different failure modes. We take a multidimensional view on UQ by stacking complementary UQ measures into a vector. Such vectors are assigned with Monge-Kantorovich ranks produced by an optimal-transport-based ordering method. The prediction is then deemed more uncertain than the other if it has a higher rank. The resulting VecUQ-OT algorithm uses entropy-regularized optimal transport. The transport map is learned on vectors of scores from in-distribution data and, by design, applies to unseen inputs, including out-of-distribution cases, without retraining. Our framework supports flexible non-additive uncertainty fusion (including aleatoric and epistemic components). It yields a robust ordering for downstream tasks such as selective prediction, misclassification detection, out-of-distribution detection, and selective generation. Across synthetic, image, and text data, VecUQ-OT shows high efficiency even when individual measures fail. The code for the method is available at: https://github.com/stat-ml/multidimensional_uncertainty.

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