Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs, addressing the challenge of label scarcity. However, existing GDA methods typically assume that both source and target graphs exhibit homophily, leading existing methods to perform poorly when heterophily is present. Furthermore, the lack of labels in the target graph makes it impossible to assess its homophily level beforehand. To address this challenge, we propose a novel homophily-agnostic approach that effectively transfers knowledge between graphs with varying degrees of homophily. Specifically, we adopt a divide-and-conquer strategy that first separately reconstructs highly homophilic and heterophilic variants of both the source and target graphs, and then performs knowledge alignment separately between corresponding graph variants. Extensive experiments conducted on five benchmark datasets demonstrate the superior performance of our approach, particularly highlighting its substantial advantages on heterophilic graphs.

Prototype-based personalized federated learning methods have emerged as a promising strategy due to their ability to represent client-specific class characteristics effectively through learned class prototypes. These prototypes capture salient features of client-local data, facilitating personalized model adaptation. However, existing prototype-based aggregation strategies predominantly rely on weighted averaging, implicitly assuming prototype consistency across clients. This assumption neglects the intrinsic heterogeneity and non-independent and identically distributed (non-IID) nature of client data, compelling diverse local prototypes to align toward a singular global prototype and consequently causing significant aggregation bias. Motivated by observations from intra-class feature saliency analysis, we identify that clients inherently emphasize distinct feature regions even for the same class. To leverage this intra-class diversity, we introduce FedIC, a novel prototype clustering and collaborative classifier optimization approach. Specifically, FedIC first clusters prototypes based on intra-class similarity to form intra-class prototype subspaces, ensuring that aggregation occurs exclusively within each cluster, thus eliminating the bias stemming from forced global unification. To further exploit the benefits of intra-cluster collaboration, we quantify the combined predictive gains of classifiers from clients within the same cluster as a function of classifier combination weights. This targeted aggregation and collaborative optimization strategy effectively circumvents the bias introduced by global alignment. Extensive experiments under various non-IID settings show that FedIC significantly outperforms existing Prototype-based and Clustered PFL Methods.

Deep imbalanced regression (DIR), where the target values have a highly skewed distribution and are also continuous, is an intriguing yet under-explored problem in machine learning. While recent works have already shown that incorporating various classification-based regularizers can produce enhanced outcomes, the role of classification remains elusive in DIR. Moreover, such regularizers (e.g., contrastive penalties) merely focus on learning discriminative features of data, which inevitably results in ignorance of either continuity or similarity across the data. To address these issues, we first bridge the connection between the objectives of DIR and classification from a Bayesian perspective. Consequently, this motivates us to decompose the objective of DIR into a combination of classification and regression tasks, which naturally guides us toward a divide-and-conquer manner to solve the DIR problem. Specifically, by aggregating the data at nearby labels into the same groups, we introduce an ordinal group-aware contrastive learning loss along with a multi-experts regressor to tackle the different groups of data thereby maintaining the data continuity. Meanwhile, considering the similarity between the groups, we also propose a symmetric descending soft labeling strategy to exploit the intrinsic similarity across the data, which allows classification to facilitate regression more effectively. Extensive experiments on real-world datasets also validate the effectiveness of our method.

Federated learning (FL) facilitates collaborative global model training without compromising data privacy. However, data distribution variations among clients inevitably introduce bias in global updates, impacting model fairness and performance. Existing methods assign client aggregation weights simply based on dataset size proportions or rely on substantial assumptions about specific global data distributions such as uniform label distributions. These approaches inadequately capture the intrinsic impact of Non-IID data characteristics on model divergence. To address these deficiencies, we propose a novel adaptive weight allocation algorithm, FedFMD, leveraging Mahalanobis distance, integrating Task Arithmetic, to dynamically assign weights based on client contributions. FedFMD explicitly models task-centric deviations caused by data heterogeneity without requiring raw data access or prior distribution assumptions. Besides, FedFMD enhances aggregation weights computation through time-decay adjustments, guided by historical client performance trends, optimizing both fairness and utility. Extensive evaluations against six state-of-the-art (SOTA) algorithms and two distance metrics across three datasets demonstrate the superior performance of FedFMD in fairness and utility.

Graph Domain Adaptation (GDA) addresses a pressing challenge in cross-network learning, particularly pertinent due to the absence of labeled data in real-world graph datasets. Recent studies attempted to learn domain invariant representations by eliminating structural shifts between graphs. In this work, we show that existing methodologies have overlooked the significance of the graph node attribute, a pivotal factor for graph domain alignment. Specifically, we first reveal the impact of node attributes for GDA by theoretically proving that in addition to the graph structural divergence between the domains, the node attribute discrepancy also plays a critical role in GDA. Moreover, we also empirically show that the attribute shift is more substantial than the topology shift, which further underscore the importance of node attribute alignment in GDA. Inspired by this finding, a novel cross-channel module is developed to fuse and align both views between the source and target graphs for GDA. Experimental results on a variety of benchmark verify the effectiveness of our method.

Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs, addressing the challenge of label scarcity. In this paper, we highlight the significance of graph homophily, a pivotal factor for graph domain alignment, which, however, has long been overlooked in existing approaches. Specifically, our analysis first reveals that homophily discrepancies exist in benchmarks. Moreover, we also show that homophily discrepancies degrade GDA performance from both empirical and theoretical aspects, which further underscores the importance of homophily alignment in GDA. Inspired by this finding, we propose a novel homophily alignment algorithm that employs mixed filters to smooth graph signals, thereby effectively capturing and mitigating homophily discrepancies between graphs. Experimental results on a variety of benchmarks verify the effectiveness of our method.

Recent source-free domain adaptation (SFDA) methods have focused on learning meaningful cluster structures in feature space, successfully adapting the knowledge from the source domain to the unlabeled target domain without accessing the private source data. However, existing methods rely on pseudo-labels generated by source models that can be noisy due to domain shift, presenting a significant challenge to their efficacy. In this paper, we study SFDA from the perspective of learning with label noise (LLN) and prove that the label noise in SFDA, unlike in conventional LLN scenarios, follows a different distribution assumption. This discrepancy renders some existing LLN methods less effective in SFDA. To address this issue and comprehensively improve adaptation performance, we tackle label noise in SFDA from two perspectives. First, we demonstrate that the early-time training phenomenon (ETP), previously observed in LLN settings, still exists in SFDA. Hence, we introduce a simple yet effective approach to leveraging ETP to improve current SFDA algorithms. Second, we propose a noise and variance control module, mitigating the label noise discrepancy between SFDA and LLN and enhancing the effectiveness of LLN methods in SFDA. Extensive empirical evaluation and analysis of four benchmarks show that our methods substantially outperform existing baselines.

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 Neural 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.

In this article, we present an analysis of unsupervised domain adaptation with a series of theoretical and algorithmic results. We derive a novel Rényi-$\alpha$divergence-based generalization bound, which is tailored to domain adaptation algorithms with arbitrary loss functions in a stochastic setting. Moreover, our theoretical results provide new insights into the assumptions for successful domain adaptation: the closeness between the conditional distributions of the domains and the Lipschitzness on the source domain. With these assumptions, we reveal the following: if their conditional generation distributions are close, the Lipschitzness property of the target domain can be transferred from the Lipschitzness on the source domain, without knowing the exact target distribution. Motivated by our analysis and assumptions, we further derive practical principles for deep domain adaptation: 1) Rényi-2 adversarial training for marginal distributions matching and 2) Lipschitz regularization for the classifier. Our experimental results on both synthetic and real-world datasets support our theoretical findings and the practical efficiency of the proposed principles.