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OT Score: An OT based Confidence Score for Source Free Unsupervised Domain Adaptation

Yiming Zhang, Sitong Liu, Alex Cloninger

TL;DR

This work addresses confidence estimation in source-free unsupervised domain adaptation by introducing the $OT$ score, a principled confidence metric derived from semi-discrete Optimal Transport that measures the extent to which a pseudo-labeled target sample aligns with label-preserving transport. It provides theoretical conditions under which OT preserves class labels and a practical, computable post-hoc criterion $g(x)$ to assess per-sample confidence, enabling selective filtering. The $OT$ score is deployed for training-time reweighting and as a label-free proxy for target performance, improving SFUDA accuracy and model selection without target labels. Empirical results across standard benchmarks show $OT$ score outperforms existing confidence metrics and yields robust gains in SFUDA tasks while maintaining computational efficiency via semi-discrete OT.

Abstract

We address the computational and theoretical limitations of current distributional alignment methods for source-free unsupervised domain adaptation (SFUDA). In particular, we focus on estimating classification performance and confidence in the absence of target labels. Current theoretical frameworks for these methods often yield computationally intractable quantities and fail to adequately reflect the properties of the alignment algorithms employed. To overcome these challenges, we introduce the Optimal Transport (OT) score, a confidence metric derived from a novel theoretical analysis that exploits the flexibility of decision boundaries induced by Semi-Discrete Optimal Transport alignment. The proposed OT score is intuitively interpretable and theoretically rigorous. It provides principled uncertainty estimates for any given set of target pseudo-labels. Experimental results demonstrate that OT score outperforms existing confidence scores. Moreover, it improves SFUDA performance through training-time reweighting and provides a reliable, label-free proxy for model performance.

OT Score: An OT based Confidence Score for Source Free Unsupervised Domain Adaptation

TL;DR

This work addresses confidence estimation in source-free unsupervised domain adaptation by introducing the score, a principled confidence metric derived from semi-discrete Optimal Transport that measures the extent to which a pseudo-labeled target sample aligns with label-preserving transport. It provides theoretical conditions under which OT preserves class labels and a practical, computable post-hoc criterion to assess per-sample confidence, enabling selective filtering. The score is deployed for training-time reweighting and as a label-free proxy for target performance, improving SFUDA accuracy and model selection without target labels. Empirical results across standard benchmarks show score outperforms existing confidence metrics and yields robust gains in SFUDA tasks while maintaining computational efficiency via semi-discrete OT.

Abstract

We address the computational and theoretical limitations of current distributional alignment methods for source-free unsupervised domain adaptation (SFUDA). In particular, we focus on estimating classification performance and confidence in the absence of target labels. Current theoretical frameworks for these methods often yield computationally intractable quantities and fail to adequately reflect the properties of the alignment algorithms employed. To overcome these challenges, we introduce the Optimal Transport (OT) score, a confidence metric derived from a novel theoretical analysis that exploits the flexibility of decision boundaries induced by Semi-Discrete Optimal Transport alignment. The proposed OT score is intuitively interpretable and theoretically rigorous. It provides principled uncertainty estimates for any given set of target pseudo-labels. Experimental results demonstrate that OT score outperforms existing confidence scores. Moreover, it improves SFUDA performance through training-time reweighting and provides a reliable, label-free proxy for model performance.
Paper Structure (22 sections, 11 theorems, 36 equations, 5 figures, 7 tables, 1 algorithm)

This paper contains 22 sections, 11 theorems, 36 equations, 5 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Optimal Transport and Domain Adaptation
  3. Domain Adaptation
  4. Optimal Transport
  5. General Theory of OT
  6. Semi-discrete Optimal Transport
  7. Theoretical Analysis
  8. Sufficient Conditions for Correct Classification
  9. Semi-Discrete Setting
  10. OT score Computation
  11. Applications and Empirical Evaluation
  12. AURC Comparisons
  13. OT Score Reweighting
  14. Model Comparison
  15. Conclusion and Future Work
  16. ...and 7 more sections

Key Result

Theorem 1

Under certain assumptions, with probability at least $1-\delta$ for all hypothesis $h$ and $\varsigma^{\prime}<\sqrt{2}$ the following holds: where $\lambda$ is the combined error of the ideal hypothesis $h^*$ that minimizes the combined error of $\epsilon_\mathcal{S}(h)+\epsilon_\mathcal{T}(h)$.

Figures (5)

  • Figure 1: (Left) Overlapping clusters. (Right) Separated clusters with flexible decision boundaries.
  • Figure 2: Mean OT Score vs. accuracy on Office-Home. Lines connect targets sharing the same source. Points denote individual target domains.
  • Figure 3: OT score performance on overlapping distributions.
  • Figure 4: Unbalanced clusters with p=0.5
  • Figure 5: Unbalanced clusters

Theorems & Definitions (21)

  • Theorem 1: Informal redko2017theoretical
  • Theorem 2: Kantorovich–Rubinstein Duality
  • Theorem 3: Existence of optimal transport map when $p=1$
  • Remark 1: Neural Collapse
  • Theorem 4
  • Remark 2
  • Lemma 5
  • Theorem 6
  • Remark 3
  • Corollary 7
  • ...and 11 more