Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift

Abstract: Adversarial learning has demonstrated good performance in the unsupervised domain adaptation setting, by learning domain-invariant representations. However, recent work has shown limitations of this approach when label distributions differ between the source and target domains. In this paper, we propose a new assumption, generalized label shift ($GLS$), to improve robustness against mismatched label distributions. $GLS$ states that, conditioned on the label, there exists a representation of the input that is invariant between the source and target domains. Under $GLS$, we provide theoretical guarantees on the transfer performance of any classifier. We also devise necessary and sufficient conditions for $GLS$ to hold, by using an estimation of the relative class weights between domains and an appropriate reweighting of samples. Our weight estimation method could be straightforwardly and generically applied in existing domain adaptation (DA) algorithms that learn domain-invariant representations, with small computational overhead. In particular, we modify three DA algorithms, JAN, DANN and CDAN, and evaluate their performance on standard and artificial DA tasks. Our algorithms outperform the base versions, with vast improvements for large label distribution mismatches. Our code is available at https://tinyurl.com/y585xt6j.

• The paper introduces Generalized Label Shift (GLS), a novel assumption for unsupervised domain adaptation that posits label-conditional invariant representations across domains.
• It provides theoretical guarantees for UDA under the GLS assumption and develops an error decomposition framework based on label distributions and conditional error gaps.
• Practical algorithmic enhancements like IWDAN and IWCDAN, integrating importance weighting into existing models, show significant empirical improvements on benchmark datasets with label distribution mismatches.

Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift

The paper under examination introduces an advanced approach to unsupervised domain adaptation (UDA) by addressing the mismatch in label distributions between source and target domains. Authors Tachet des Combes et al. have proposed a novel assumption known as generalized label shift (GLS) that augments the robustness of domain adaptation strategies such as adversarial learning models like Domain Adversarial Neural Networks (DANN) and Conditional Domain Adversarial Networks (CDAN).

Key Contributions

1. Generalized Label Shift (GLS): The paper defines GLS, which posits that for each label, there exists a representation of the input that remains invariant across the source and target domains. This is a relaxation from the traditional label shift that assumes invariance in the input space.
2. Theoretical Guarantees: The study provides robust proofs and theoretical guarantees under the GLS assumption which suggest that UDA algorithms could maintain performance integrity even in the presence of significant label distribution mismatches.
3. Error Decomposition Framework: Building upon the GLS, the authors develop a framework that decomposes the error between the source and target domains into terms that involve only the distribution of the labels, the balanced error rate (BER), and the conditional error gap, avoiding reliance on unobservable optimal hypothesis complexities.
4. Practical Algorithmic Enhancements: The authors propose enhancements to existing algorithms (namely DANN, CDAN, and Joint Adaptation Networks - JAN) for better generalization by integrating importance weight estimation into their adversarial loss functions. The improved versions (IWDAN, IWCDAN, and IWJAN) show substantial empirical improvements on several datasets with varying label distribution mismatches.

Experimental Evaluation

Experimental results demonstrate that the proposed approaches outperform their baseline counterparts, especially in scenarios with significant label distribution divergence, as measured by the Jensen-Shannon divergence. The variants of DANN and CDAN adapted for GLS, termed as IWDAN and IWCDAN, manifest a marked increase in accuracy across tasks and datasets including MNIST to USPS, Visda challenge, Office-31, and Office-Home.

Practical and Theoretical Implications

• Practical Utility: The methods presented offer a straightforward extension to the current UDA frameworks without the need for major architectural changes, hence could be readily adapted for real-world applications with domain shifts, such as object recognition systems transitioning from synthetic to real-world scenarios.
• Theoretical Rigor in DA: The introduction of GLS brings attention towards a principled understanding of how domain-agnostic, invariant features could be optimally selected, enhancing the theoretical foundations of domain adaptation beyond conventional covariate or label shift assumptions.

Future Directions

Future work could examine the dynamics of importance weight estimation in complex systems and extend the proposed strategies to semi-supervised scenarios or settings involving multiple target domains. Additionally, extending the theoretical framework to domain generalization, where no target data is available, represents an ambitious yet impactful research trajectory.

In conclusion, this paper makes a significant contribution to the field of domain adaptation by successfully addressing the challenges posed by mismatched label distributions. The introduction of GLS as a viable assumption to improve the robustness of domain-invariant representation learning could pave the way for more resilient machine learning models capable of handling diverse and dynamic data landscapes.