Locality-aware Private Class Identification for Domain Adaptation with Extreme Label Shift

Technical Summary: Locality-aware Private Class Identification for Domain Adaptation with Extreme Label Shift

Problem Statement
Unsupervised Domain Adaptation (UDA) typically assumes a closed-set scenario where source and target domains share an identical label space. However, real-world applications often involve "extreme label shift," where the label spaces are heterogeneous. This manifests in two primary scenarios: Open Set Domain Adaptation (OSDA), where the target domain contains private classes absent in the source, and Partial Domain Adaptation (PDA), where the source domain contains private classes absent in the target.

The core challenge in these scenarios is "private class identification." Existing methods generally rely on the assumption that the semantic shift of private classes is consistently larger than the domain shift of shared classes, treating private samples as outliers. The authors argue this assumption is often violated in practice, as the variance within a single shared class can exceed the gap between a private class and another shared class. Consequently, existing methods often fail to reliably distinguish private samples, leading to negative transfer and misalignment.

Methodology
The paper proposes a novel framework centered on Locality-aware Private Class Identification and a reliable transfer model named ReOT (Reliable OT-based method).

1. Locality-aware Identification via Masked Optimal Transport (MOT):

   • The authors observe that while global shifts may be ambiguous, a local spatial structure holds: within a local neighborhood of a shared class cluster, the distance between shared samples is consistently smaller than the distance between shared and private samples.
   • They utilize Masked Optimal Transport (MOT) to characterize this local structure. A mask matrix is applied to the cost matrix to enforce transport only between samples with the same predicted labels.
   • A transport mass-based score function is derived. Based on the theoretical properties of MOT, the total mass transported to a private class sample from a shared class source is significantly smaller than the mass transported to a shared class sample.
   • A score $s(z')$ is defined as $1/m - \sum \Gamma^*_{ij}$. Samples with $s(z') > 0$ (or exceeding a margin) are identified as private, while those with $s(z') < 0$ are identified as shared. This approach theoretically guarantees the separation of shared and private samples under local spatial assumptions without relying on global outlier assumptions.

2. The ReOT Framework:

   • Reliable Transfer Loss ($L_{rt}$): Once private and shared samples are identified, ReOT minimizes the cross-domain intra-class distances for shared classes while maximizing the distance between shared and private classes. This is achieved using the transport plan from MOT to align conditional distributions only within the identified shared sets.
   • Risk Minimization ($L_{cls}$): The model minimizes empirical classification risk on both the source domain and the identified private samples in the target (or source, for PDA) domain.
   • Barycenter Reconstruction Loss ($L_{br}$): To further refine the representation, the model maps target representations back to the source domain using the transport plan (barycenter map) and minimizes the reconstruction loss. This provides soft supervision, pushing target samples toward their corresponding class prototypes.
   • The final objective combines these losses: $L = L_{cls} + \eta_1 L_{rt} + \eta_2 L_{br}$.

3. Theoretical Analysis:

   • The paper provides a generalization upper bound for the target risk in extreme label shift scenarios. The bound decomposes the error into terms related to source risk, maximal prediction error, label distribution discrepancy, and the shared conditional gap.
   • The authors prove that ReOT minimizes this upper bound by reducing the source risk, aligning conditional distributions (reducing the shared conditional gap), and effectively identifying private classes to minimize errors on those specific samples.

Key Contributions

• Locality-aware Identification: A new method for identifying private classes using a score function derived from MOT transport mass. It relaxes the unrealistic global outlier assumption by leveraging local spatial structures.
• Theoretical Guarantee: A theoretical proof demonstrating the score function's ability to distinguish shared and private samples, and a generalization error bound for extreme label shift scenarios that ReOT is shown to minimize.
• Unified Framework (ReOT): A single algorithm capable of handling both OSDA and PDA settings by dynamically adjusting the transport direction and mask definitions based on which domain contains the private classes.
• Empirical Validation: Extensive experiments on four benchmark datasets (Image-CLEF, Office-31, Office-Home, VisDA-2017) demonstrating superior performance over state-of-the-art methods in both OSDA and PDA settings.

Experimental Results

• OSDA Performance: On Image-CLEF, Office-31, and Office-Home, ReOT achieved the highest harmonic mean ($H$) accuracy in the majority of tasks, outperforming SOTA methods like ANNA and MRJT. For instance, on Image-CLEF, ReOT achieved an average $H$ of 84.4%, surpassing ANNA by 1.5%.
• PDA Performance: ReOT demonstrated robust performance on Office-Home and VisDA-2017, achieving the best mean accuracy (78.7% on Office-Home) and maintaining high performance on the challenging VisDA-2017 dataset where other methods degraded significantly.
• Ablation Studies: Removing the transfer loss ($L_{rt}$) or reconstruction loss ($L_{br}$) resulted in performance drops, confirming the necessity of both class-conditional alignment and barycenter reconstruction.
• Identification Efficiency: The private class identification method successfully identified approximately 88.2% of private samples in OSDA and 95.6% in PDA across datasets.
• Robustness: The method remained stable across different hyper-parameter settings and cost function choices (squared Euclidean vs. discriminator-based).

Significance and Claims
The paper claims that ReOT addresses the fundamental limitation of existing private class identification methods by shifting the focus from global outlier detection to local spatial structure characterization. By theoretically grounding the identification process in the properties of masked optimal transport, the method ensures reliability even when private classes are not distinct outliers.

The authors assert that ReOT provides a unified solution for both OSDA and PDA, bridging the gap between these two symmetric but often treated separately scenarios. Theoretically, the proposed generalization bound offers a new perspective on decomposing error in heterogeneous label spaces, showing that minimizing the bound requires both accurate private class identification and conditional distribution alignment. Empirically, the results validate that ReOT achieves a better balance between recognizing private samples and preserving the performance of shared classes, leading to more robust domain adaptation in real-world, extreme label shift scenarios.

The paper concludes modestly, noting that while ReOT is effective for single-source/single-target scenarios, future work could extend the framework to multi-source, multi-target, and source-free settings.