Reproduce “Multidimensional Uncertainty Quantification via Optimal Transport” on OpenResearch

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About this paper

Nikita Kotelevskii, Maiya Goloburda, Vladimir Kondratyev, Alexander Fishkov, Mohsen Guizani, Eric Moulines, Maxim Panov

The paper presents a method that combines multiple uncertainty scores into a single ranking using entropy-regularized optimal transport. It maps score vectors from unlabeled calibration inputs to a reference distribution and ranks new inputs by distance from its center. In a synthetic logistic-regression test, it achieved perfect out-of-distribution detection while retaining 0.710 misclassification-detection ROC-AUC, but did not lead both tasks.

Key insights

  • A multidimensional representation of uncertainty, created by combining diverse measures, offers a more comprehensive and robust view of model reliability than single-scalar approaches.
  • Optimal Transport provides a theoretically grounded, non-parametric mechanism to establish a principled ordering for complex, multivariate uncertainty signals.
  • The framework acts as a 'label-free calibration layer,' intelligently fusing multiple signals to simplify UQ integration into machine learning workflows for various downstream tasks without needing task-specific re-tuning.

Summary by alphaXiv.

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