Regularized Learning for Domain Adaptation under Label Shifts (1903.09734v1)

Abstract: We propose Regularized Learning under Label shifts (RLLS), a principled and a practical domain-adaptation algorithm to correct for shifts in the label distribution between a source and a target domain. We first estimate importance weights using labeled source data and unlabeled target data, and then train a classifier on the weighted source samples. We derive a generalization bound for the classifier on the target domain which is independent of the (ambient) data dimensions, and instead only depends on the complexity of the function class. To the best of our knowledge, this is the first generalization bound for the label-shift problem where the labels in the target domain are not available. Based on this bound, we propose a regularized estimator for the small-sample regime which accounts for the uncertainty in the estimated weights. Experiments on the CIFAR-10 and MNIST datasets show that RLLS improves classification accuracy, especially in the low sample and large-shift regimes, compared to previous methods.

• The paper introduces RLLS, a new method for domain adaptation that directly addresses label distribution shifts using regularized importance weight estimation.
• It derives a dimension-independent generalization bound, achieving up to 20% improvement in accuracy and F-1 score over baseline methods under severe shifts.
• Empirical tests on datasets like CIFAR-10 and MNIST demonstrate RLLS's robustness in small-sample regimes and its effective reduction of estimation error.

Regularized Learning for Domain Adaptation under Label Shifts: A Thorough Examination

In this paper, the authors propose a novel algorithm titled Regularized Learning under Label Shifts (RLLS), offering a systematic approach to domain adaptation in scenarios marked by shifts in label distributions between source and target domains. Addressing the limitations of traditional models trained under the covariate shift assumption, this paper shifts the focus to label shifts, a less-explored yet significant aspect of domain adaptation.

The core of the RLLS method lies in its capacity to adjust the label distribution discrepancies between two domains by estimating importance weights using labeled data from the source domain and unlabeled data from the target domain. Subsequently, RLLS trains a classifier on the weighted source samples, introducing a key innovation— a generalization bound for the target domain classifier independent of the data dimensionality, relying solely on function class complexity. Notably, this represents the first derivation of such a generalization bound in label-shift contexts absent target domain labels.

RLLS applies regularization to address the substantial estimation errors inherent in small sample regimes, thereby enhancing the robustness of its weight estimator. Through empirical validations on prominent datasets like CIFAR-10 and MNIST, RLLS demonstrates superior classification accuracy, particularly in conditions of low sample counts and pronounced shifts, as compared to existing methods.

Methodological Developments

The paper delineates two predominant domain adaptation scenarios: covariate shift and label shift. In the label shift context, the assumption that $p(x|y) = q(x|y)$ holds, while $p(y) \neq q(y)$. This presents a computationally feasible setting given the lower dimensionality of outputs compared to inputs.

RLLS introduces an efficient plug-in weight estimator, tailored for small sample settings by regularization methods that compensate for the high estimation variance. This facilitates improved empirical risk minimization when applying estimated weights in the training process. Furthermore, the authors establish a dimension-independent generalization bound for the RLLS classifier, significantly outperforming baseline methods on error estimation premises, especially in high-shift conditions or with limited samples.

Numerical Results

The findings exhibit RLLS's proficiency with an order of magnitude reduction in weight estimation error over baseline methods and substantial improvements (up to 20% in accuracy and F-1 score) in predictive tasks under severe label shifts. Additionally, RLLS demonstrates resilience in low target sample settings by effectively adjusting its regularization parameters.

Theoretical and Practical Implications

The development of the RLLS method is particularly relevant for real-world machine learning applications deployed across varied datasets where label distributions can diverge sharply from training data. For instance, RLLS could significantly benefit cloud service models or medical diagnostic systems operating across diverse geographic and demographic profiles.

Moreover, the theoretical contributions of this work lie in extending domain adaptation research into label-shift scenarios and providing strong generalization guarantees, a pioneering achievement in literature. The paper's insight enriches understanding of supervised learning amid distributional shifts, laying groundwork for future exploration in adaptable machine learning frameworks.

Future Directions

Despite its contributions, the paper acknowledges potential avenues for further inquiry, including exploring situations where the label shift assumption marginally falters. Integrating the RLLS framework within an active learning paradigm, where acquiring a limited number of labels from the target dataset may significantly enhance model performance, constitutes a promising extension. Understanding the model's behavior in overparameterized settings or within cost-sensitive environments could also enhance its applicability and robustness across broader contexts.

In conclusion, this paper's advancement of RLLS enriches the theoretical and practical toolbox for addressing domain adaptation under label shifts, setting a benchmark for future research to expand and refine these methodologies.