Generalizing across Temporal Domains with Koopman Operators

In the field of domain generalization, the task of constructing a predictive model capable of generalizing to a target domain without access to target data remains challenging. This problem becomes further complicated when considering evolving dynamics between domains. While various approaches have been proposed to address this issue, a comprehensive understanding of the underlying generalization theory is still lacking. In this study, we contribute novel theoretic results that aligning conditional distribution leads to the reduction of generalization bounds. Our analysis serves as a key motivation for solving the Temporal Domain Generalization (TDG) problem through the application of Koopman Neural Operators, resulting in Temporal Koopman Networks (TKNets). By employing Koopman Operators, we effectively address the time-evolving distributions encountered in TDG using the principles of Koopman theory, where measurement functions are sought to establish linear transition relations between evolving domains. Through empirical evaluations conducted on synthetic and real-world datasets, we validate the effectiveness of our proposed approach.

When Source-Free Domain Adaptation Meets Learning with Noisy Labels

Recent state-of-the-art source-free domain adaptation (SFDA) methods have focused on learning meaningful cluster structures in the feature space, which have succeeded in adapting the knowledge from source domain to unlabeled target domain without accessing the private source data. However, existing methods rely on the pseudo-labels generated by source models that can be noisy due to domain shift. In this paper, we study SFDA from the perspective of learning with label noise (LLN). Unlike the label noise in the conventional LLN scenario, we prove that the label noise in SFDA follows a different distribution assumption. We also prove that such a difference makes existing LLN methods that rely on their distribution assumptions unable to address the label noise in SFDA. Empirical evidence suggests that only marginal improvements are achieved when applying the existing LLN methods to solve the SFDA problem. On the other hand, although there exists a fundamental difference between the label noise in the two scenarios, we demonstrate theoretically that the early-time training phenomenon (ETP), which has been previously observed in conventional label noise settings, can also be observed in the SFDA problem. Extensive experiments demonstrate significant improvements to existing SFDA algorithms by leveraging ETP to address the label noise in SFDA.

On Learning Fairness and Accuracy on Multiple Subgroups

We propose an analysis in fair learning that preserves the utility of the data while reducing prediction disparities under the criteria of group sufficiency. We focus on the scenario where the data contains multiple or even many subgroups, each with limited number of samples. As a result, we present a principled method for learning a fair predictor for all subgroups via formulating it as a bilevel objective. Specifically, the subgroup specific predictors are learned in the lower-level through a small amount of data and the fair predictor. In the upper-level, the fair predictor is updated to be close to all subgroup specific predictors. We further prove that such a bilevel objective can effectively control the group sufficiency and generalization error. We evaluate the proposed framework on real-world datasets. Empirical evidence suggests the consistently improved fair predictions, as well as the comparable accuracy to the baselines.

Evolving Domain Generalization

Domain generalization aims to learn a predictive model from multiple different but related source tasks that can generalize well to a target task without the need of accessing any target data. Existing domain generalization methods ignore the relationship between tasks, implicitly assuming that all the tasks are sampled from a stationary environment. Therefore, they can fail when deployed in an evolving environment. To this end, we formulate and study the \emph{evolving domain generalization} (EDG) scenario, which exploits not only the source data but also their evolving pattern to generate a model for the unseen task. Our theoretical result reveals the benefits of modeling the relation between two consecutive tasks by learning a globally consistent directional mapping function. In practice, our analysis also suggests solving the DDG problem in a meta-learning manner, which leads to \emph{directional prototypical network}, the first method for the DDG problem. Empirical evaluation of both synthetic and real-world data sets validates the effectiveness of our approach.