As a crucial data mining problem, domain adaptation (DA) under dataset shift offers an effective paradigm for transferring knowledge in changing environments (i.e., shifting data distributions). Recent theoretical advances show that learning conditional information is crucial for successful DA, and empirical models with provable performance have been developed under discrete priors. However, for many real-world complex tasks with continuous label spaces, e.g., regression, conditional information is generally intractable, and shift correction models remain unexplored due to the high-dimensional nature of continuous variables. To deal with these challenges, we propose an information-theoretic learning principle called bi-level conditional dependence (BiCD) for continuous shift setting. BiCD characterizes the conditional information of learned representations from two aspects: conditional domain dependence and conditional label dependence, where our results prove that bi-level dependence learning is sufficient to obtain representations with desired properties and to minimize the generalization error. Moreover, BiCD also admits appealing properties for practical modeling: 1) an equivalent formulation with marginal dependence is derived to avoid the explicit computation of high-dimensional conditional dependence in practical modeling; 2) a kernel dependence-based variant is developed to serve as a guaranteed numerical proxy for the vanilla BiCD; 3) a graph Laplacian understanding is provided to justify the learning mechanism of BiCD. Empirically, BiCD is evaluated on standard DA regression datasets, where the significance of the proposed dependence learning principle is validated and SOTA performance is consistently achieved.

Optimal transport (OT) is a rising research area to overcome distribution shifts in real-world data, which has been widely applied in visual signal processing tasks due to its appealing mathematical properties. However, previous works 1) consider the transport cost in Euclidean space, which conflicts with the well-known manifold prior on intrinsic data structure; 2) only consider first-order relation between inputs, which is infeasible for severe shift with heterogeneous spaces. These limitations usually disrupt the manifold structure and degrade the generalization performance on the test data. To deal with these issues, we propose the manifold preserving OT (MPOT) on Gromov-Wasserstein (GW), which introduces 1) the graph-based cost formulation for high-order relation characterization; 2) relation modeling for unshared knowledge between heterogeneous spaces. Mathematically, by encoding the high-order edge information as binary pattern, the GW-based regularization is developed to capture the intrinsic structure for label discriminability. Numerical algorithm with theoretical guarantee is provided, which ensures that MPOT can be efficiently solved by block coordinate descent. Extensive experiments validate MPOT for cross-domain visual classification with changing label spaces.

As an important learning paradigm for signal processing and pattern recognition, unsupervised domain adaptation (UDA), which deals with the learning bias induced by the changing data environments (i.e., domains), has achieved great success in real-world applications. Mainstream UDA methods commonly adopt the discrepancy optimization on the two data domains directly, which ignore the hidden information in the latent intermediate domains and cannot sufficiently learn the invariant knowledge across domains; moreover, they usually fail when the domain gap is significant. In this work, a novel learning principle called Wasserstein invariant risk (WIR) is developed to gradually reduce the bias. The core idea is to recover the latent domains along the Wasserstein geodesic with local structure preservation, and explicitly map them into an invariant space via barycenter mapping. Intuitively, the Wasserstein geodesic captures the non-Euclidean structures of the latent domains. Methodologically, the barycenter mapping along geodesic can: 1) reduce the data discrepancy gradually and explore the hidden information; 2) ensure the consistency of risk estimation across domains; 3) admit invariance property of learning model for changing environments. Extensive experiments on visual UDA classification show the superiority of WIR over SOTA methods.

Reinforcement Learning (RL) has emerged as a powerful tool for neural combinatorial optimization, enabling models to learn heuristics that solve complex problems without requiring expert knowledge. Despite significant progress, existing RL approaches face challenges such as diminishing reward signals and inefficient exploration in vast combinatorial action spaces, leading to inefficiency. In this paper, we propose **Preference Optimization**, a novel method that transforms quantitative reward signals into qualitative preference signals via statistical comparison modeling, emphasizing the superiority among sampled solutions. Methodologically, by reparameterizing the reward function in terms of policy and utilizing preference models, we formulate an entropy-regularized RL objective that aligns the policy directly with preferences while avoiding intractable computations. Furthermore, we integrate local search techniques into the fine-tuning rather than post-process to generate high-quality preference pairs, helping the policy escape local optima. Empirical results on various benchmarks, such as the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP) and the Flexible Flow Shop Problem (FFSP), demonstrate that our method significantly outperforms existing RL algorithms, achieving superior convergence efficiency and solution quality.

Partial domain adaptation (PDA) is a challenging task in real-world machine learning scenarios. It aims to transfer knowledge from a labeled source domain to a related unlabeled target domain, where the support set of the source label distribution subsumes the target one. Previous PDA works managed to correct the label distribution shift by weighting samples in the source domain. However, the simple reweighing technique cannot explore the latent structure and sufficiently use the labeled data, and then models are prone to over-fitting on the source domain. In this work, we propose a novel importance sampling-based shift correction (IS2C) method, where new labeled data are sampled from a built sampling domain, whose label distribution is supposed to be the same as the target domain, to characterize the latent structure and enhance the generalization ability of the model. We provide theoretical guarantees for IS2C by proving that the generalization error can be sufficiently dominated by IS2C. In particular, by implementing sampling with the mixture distribution, the extent of shift between source and sampling domains can be connected to generalization error, which provides an interpretable way to build IS2C. To improve knowledge transfer, an optimal transport-based independence criterion is proposed for conditional distribution alignment, where the computation of the criterion can be adjusted to reduce the complexity from $\mathcal {O}(n^{3})$ to $\mathcal {O}(n^{2})$ in realistic PDA scenarios. Extensive experiments on PDA benchmarks validate the theoretical results and demonstrate the effectiveness of our IS2C over existing methods.

Optimal transport (OT) is an important methodology to measure distribution discrepancy, which has achieved promising performance in artificial intelligence applications, e.g., unsupervised domain adaptation. However, from the view of transportation, there are still limitations: 1) the local discriminative structures for downstream tasks, e.g., cluster structure for classification, cannot be explicitly admitted by the learned OT plan; 2) the entropy regularization induces a dense OT plan with increasing uncertainty. To tackle these issues, we propose a novel Probability-Polarized OT (PPOT) framework, which can characterize the structure of OT plan explicitly. Specifically, the probability polarization mechanism is proposed to guide the optimization direction of OT plan, which generates a clear margin between similar and dissimilar transport pairs and reduces the uncertainty. Further, a dynamic mechanism for margin is developed by incorporating task-related information into the polarization, which directly captures the intra/inter class correspondence for knowledge transportation. A mathematical understanding for PPOT is provided from the view of gradient, which ensures interpretability. Extensive experiments on several datasets validate the effectiveness and empirical efficiency of PPOT.

As a crucial step toward real-world learning scenarios with changing environments, dataset shift theory and invariant representation learning algorithm have been extensively studied to relax the identical distribution assumption in classical learning setting. Among the different assumptions on the essential of shifting distributions, generalized label shift (GLS) is the latest developed one which shows great potential to deal with the complex factors within the shift. In this paper, we aim to explore the limitations of current dataset shift theory and algorithm, and further provide new insights by presenting a comprehensive understanding of GLS. From theoretical aspect, two informative generalization bounds are derived, and the GLS learner are proved to be sufficiently close to optimal target model from the Bayesian perspective. The main results show the insufficiency of invariant representation learning, and prove the sufficiency and necessity of GLS correction for generalization, which provide theoretical supports and innovations for exploring generalizable model under dataset shift. From methodological aspect, we provide a unified view of existing shift correction frameworks, and propose a kernel embedding-based correction algorithm (KECA) to minimize the generalization error and achieve successful knowledge transfer. Both theoretical results and extensive experiment evaluations demonstrate the sufficiency and necessity of GLS correction for addressing dataset shift and the superiority of proposed algorithm.

To overcome the restriction of identical distribution assumption, invariant representation learning for unsupervised domain adaptation (UDA) has made significant advances in computer vision and pattern recognition communities. In UDA scenario, the training and test data belong to different domains while the task model is learned to be invariant. Recently, empirical connections between transferability and discriminability have received increasing attention, which is the key to understand the invariant representations. However, theoretical study of these abilities and in-depth analysis of the learned feature structures are unexplored yet. In this work, we systematically analyze the essentials of transferability and discriminability from the geometric perspective. Our theoretical results provide insights into understanding the co-regularization relation and prove the possibility of learning these abilities. From methodology aspect, the abilities are formulated as geometric properties between domain/cluster subspaces (i.e., orthogonality and equivalence) and characterized as the relation between the norms/ranks of multiple matrices. Two optimization-friendly learning principles are derived, which also ensure some intuitive explanations. Moreover, a feasible range for the co-regularization parameters is deduced to balance the learning of geometric structures. Based on the theoretical results, a geometry-oriented model is proposed for enhancing the transferability and discriminability via nuclear norm optimization. Extensive experiment results validate the effectiveness of the proposed model in empirical applications, and verify that the geometric abilities can be sufficiently learned in the derived feasible range.

As an important methodology to measure distribution discrepancy, optimal transport (OT) has been successfully applied to learn generalizable visual models under changing environments. However, there are still limitations, including strict prior assumption and implicit alignment, for current OT modeling in challenging real-world scenarios like partial domain adaptation, where the learned trans-port plan may be biased and negative transfer is inevitable. Thus, it is necessary to explore a more feasible OT methodology for real-world applications. In this work, we focus on the rigorous OT modeling for conditional distribution matching and label shift correction. A novel masked OT (MOT) methodology on conditional distributions is proposed by defining a mask operation with label information. Further, a relaxed and reweighting formulation is proposed to improve the robustness of OT in extreme scenarios. We prove the theoretical equivalence between conditional OT and MOT, which implies the well-defined MOT serves as a computation-friendly proxy. Extensive experiments validate the effectiveness of theoretical results and proposed model.

As a fundamental manner for learning and cognition, transfer learning has attracted widespread attention in recent years. Typical transfer learning tasks include unsupervised domain adaptation (UDA) and few-shot learning (FSL), which both attempt to sufficiently transfer discriminative knowledge from the training environment to the test environment to improve the model's generalization performance. Previous transfer learning methods usually ignore the potential conditional distribution shift between environments. This leads to the discriminability degradation in the test environments. Therefore, how to construct a learnable and interpretable metric to measure and then reduce the gap between conditional distributions is very important in the literature. In this article, we design the Conditional Kernel Bures (CKB) metric for characterizing conditional distribution discrepancy, and derive an empirical estimation with convergence guarantee. CKB provides a statistical and interpretable approach, under the optimal transportation framework, to understand the knowledge transfer mechanism. It is essentially an extension of optimal transportation from the marginal distributions to the conditional distributions. CKB can be used as a plug-and-play module and placed onto the loss layer in deep networks, thus, it plays the bottleneck role in representation learning. From this perspective, the new method with network architecture is abbreviated as BuresNet, and it can be used extract conditional invariant features for both UDA and FSL tasks. BuresNet can be trained in an end-to-end manner. Extensive experiment results on several benchmark datasets validate the effectiveness of BuresNet.

Unsupervised domain adaptation is effective in leveraging rich information from a labeled source domain to an unlabeled target domain. Though deep learning and adversarial strategy made a significant breakthrough in the adaptability of features, there are two issues to be further studied. First, hard-assigned pseudo labels on the target domain are arbitrary and error-prone, and direct application of them may destroy the intrinsic data structure. Second, batch-wise training of deep learning limits the characterization of the global structure. In this paper, a Riemannian manifold learning framework is proposed to achieve transferability and discriminability simultaneously. For the first issue, this framework establishes a probabilistic discriminant criterion on the target domain via soft labels. Based on pre-built prototypes, this criterion is extended to a global approximation scheme for the second issue. Manifold metric alignment is adopted to be compatible with the embedding space. The theoretical error bounds of different alignment metrics are derived for constructive guidance. The proposed method can be used to tackle a series of variants of domain adaptation problems, including both vanilla and partial settings. Extensive experiments have been conducted to investigate the method and a comparative study shows the superiority of the discriminative manifold learning framework.

As a vital problem in classification-oriented transfer, unsupervised domain adaptation (UDA) has attracted widespread attention in recent years. Previous UDA methods assume the marginal distributions of different domains are shifted while ignoring the discriminant information in the label distributions. This leads to classification performance degeneration in real applications. In this work, we focus on the conditional distribution shift problem which is of great concern to current conditional invariant models. We aim to seek a kernel covariance embedding for conditional distribution which remains yet unexplored. Theoretically, we propose the Conditional Kernel Bures (CKB) metric for characterizing conditional distribution discrepancy, and derive an empirical estimation for the CKB metric without introducing the implicit kernel feature map. It provides an interpretable approach to understand the knowledge transfer mechanism. The established consistency theory of the empirical estimation provides a theoretical guarantee for convergence. A conditional distribution matching network is proposed to learn the conditional invariant and discriminative features for UDA. Extensive experiments and analysis show the superiority of our proposed model.

Unsupervised domain adaptation is effective in leveraging the rich information from the source domain to the unsupervised target domain. Though deep learning and adversarial strategy make an important breakthrough in the adaptability of features, there are two issues to be further explored. First, the hard-assigned pseudo labels on the target domain are risky to the intrinsic data structure. Second, the batch-wise training manner in deep learning limits the description of the global structure. In this paper, a Riemannian manifold learning framework is proposed to achieve transferability and discriminability consistently. As to the first problem, this method establishes a probabilistic discriminant criterion on the target domain via soft labels. Further, this criterion is extended to a global approximation scheme for the second issue; such approximation is also memory-saving. The manifold metric alignment is exploited to be compatible with the embedding space. A theoretical error bound is derived to facilitate the alignment. Extensive experiments have been conducted to investigate the proposal and results of the comparison study manifest the superiority of consistent manifold learning framework.

Unsupervised domain adaptation (UDA) is a representative problem in transfer learning, which aims to improve the classification performance on an unlabeled target domain by exploiting discriminant information from a labeled source domain. The optimal transport model has been used for UDA in the perspective of distribution matching. However, the transport distance cannot reflect the discriminant information from either domain knowledge or category prior. In this work, we propose an enhanced transport distance (ETD) for UDA. This method builds an attention-aware transport distance, which can be viewed as the prediction feedback of the iteratively learned classifier, to measure the domain discrepancy. Further, the Kantorovich potential variable is re-parameterized by deep neural networks to learn the distribution in the latent space. The entropy-based regularization is developed to explore the intrinsic structure of the target domain. The proposed method is optimized alternately in an end-to-end manner. Extensive experiments are conducted on four benchmark datasets to demonstrate the SOTA performance of ETD.

Image set recognition has been widely applied in many practical problems like real-time video retrieval and image caption tasks. Due to its superior performance, it has grown into a significant topic in recent years. However, images with complicated variations, e.g., postures and human ages, are difficult to address, as these variations are continuous and gradual with respect to image appearance. Consequently, the crucial point of image set recognition is to mine the intrinsic connection or structural information from the image batches with variations. In this work, a Discriminant Residual Analysis (DRA) method is proposed to improve the classification performance by discovering discriminant features in related and unrelated groups. Specifically, DRA attempts to obtain a powerful projection which casts the residual representations into a discriminant subspace. Such a projection subspace is expected to magnify the useful information of the input space as much as possible, then the relation between the training set and the test set described by the given metric or distance will be more precise in the discriminant subspace. We also propose a nonfeasance strategy by defining another approach to construct the unrelated groups, which help to reduce furthermore the cost of sampling errors. Two regularization approaches are used to deal with the probable small sample size problem. Extensive experiments are conducted on benchmark databases, and the results show superiority and efficiency of the new methods.