{"ID":2865371,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.22380","arxiv_id":"2509.22380","title":"Multidimensional Uncertainty Quantification via Optimal Transport","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.","short_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 meas...","url_abs":"https://arxiv.org/abs/2509.22380","url_pdf":"https://arxiv.org/pdf/2509.22380v1","authors":"[\"Nikita Kotelevskii\",\"Maiya Goloburda\",\"Vladimir Kondratyev\",\"Alexander Fishkov\",\"Mohsen Guizani\",\"Eric Moulines\",\"Maxim Panov\"]","published":"2025-09-26T14:09:03Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false,"code_links":[{"ID":609267,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2865371,"paper_url":"https://arxiv.org/abs/2509.22380","paper_title":"Multidimensional Uncertainty Quantification via Optimal Transport","repo_url":"https://github.com/stat-ml/multidimensional_uncertainty","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}