Label shift is a prevalent phenomenon encountered in open environments, characterized by a notable discrepancy in the label distributions between the source (training) and target (test) domains, whereas the conditional distributions given the labels remain invariant. Existing label shift methods adopt a two-step strategy: initially computing the importance weight and subsequently utilizing it to calibrate the target outputs. However, this conventional strategy overlooks the intricate interplay between output adjustment and weight estimation. In this paper, we introduce a novel approach termed as One-step Label Shift Adaptation (OLSA). Our methodology jointly learns the predictive model and the corresponding weights through a bi-level optimization framework, with the objective of minimizing an upper bound on the target risk. To enhance the robustness of our proposed model, we incorporate a debiasing term into the upper-level classifier training and devise a regularization term for the lower-level weight estimation. Furthermore, we present theoretical analyses about the generalization bounds, offering guarantees for the model's performance. Extensive experimental results substantiate the efficacy of our proposal.

Multi-view subspace clustering, which aims to partition a set of multi-source data into a common space, has recently attracted wide attention in the field of data analysis and machine learning. Traditional algorithms may face the problem of high complexity in calculating the self-expression matrix and in turning parameter. This paper proposes a novel multi-view subspace clustering model termed as Low-rank Multi-view Subspace Clustering via Adaptive Weight (LMSCAW). LMSCAW decomposes the self-expression matrix into the product of two low-rank representation matrices and thus can fix the rank of the self-expression matrix of each view to increase the stability of the algorithm. In addition, in order to learn the common representation matrix better, LMSCAW fuses the self-expression matrices among multiple views and implicitly weights each view by the Frobenius norm without additional parameters. Extensive experimental results on multiple benchmark datasets are provided to show the effectiveness of the proposed algorithm and its superior performance over other state-of-the-art methods.

In many image processing tasks, e.g., 3D reconstruction of dynamic scenes, different types of descriptions, a.k.a., views, of an object are emerging in a streaming way. Streaming view learning provides an effective solution to this dynamic view problem. In this paradigm, existing streaming view learning methods typically assume that all labels are accurate. However, in many real-world applications, the initial views may be not good enough for characterizing, leading to noisy labels that degrade classification performance. How to learn a model for simultaneous view evolving and label ambiguity is critical yet unexplored. In this paper, we propose a novel method called Streaming View Classification with Noisy Label (SVCNL). We calibrate noisy labels according to the emerging of new views, thereby reflecting the dynamic changes in the data more accurately. Leveraging the sequential and non-revisitable nature of views, the method tunes existing models to inherit information from previous stages by utilizing current-stage data. It reconstructs noisy labels through a label transition matrix and establishes relationships between true labels and samples using a graph embedding strategy, progressively correcting noisy labels. Together with the theoretical analyses about generalization bounds, extensive experiments demonstrate the effectiveness of the proposed approach.

Due to the timeliness and uncertainty of data acquisition, label shift, which assumes that the source (training) and target (test) label distributions differ, occurs with the changing environment and reduces the generalization ability of traditional models. To correct the label shift, existing methods estimate the true label distribution by prediction of target data from a source classifier, which results in high variance, especially with large label shift. In this paper, we tackle this problem by proposing a novel approach termed as Label Shift Correction via Bidirectional Marginal Distribution Matching (BMDM). Our approach matchs the label and feature marginal distributions simultaneously to ensure the stability of estimated class proportions. We prove theoretically that there is a unique optimal solution, i.e., true target label distribution, for our approach under mild conditions, and an efficient optimization strategy is also proposed. On this basis, in multi-shot scenario where label distribution changes continuously, we extend BMDM by designing a new distribution matching mechanism and constructing a regularization term that constrains the direction of label distribution change. Extensive experimental results validate the effectiveness of our approach over existing state-of-the-arts methods.

In image processing, images are usually composed of partial views due to the uncertainty of collection and how to efficiently process these images, which is called incomplete multi-view learning, has attracted widespread attention. The incompleteness and diversity of multi-view data enlarges the difficulty of annotation, resulting in the divergence of label distribution between the training and testing data, named as label shift. However, existing incomplete multi-view methods generally assume that the label distribution is consistent and rarely consider the label shift scenario. To address this new but important challenge, we propose a novel framework termed as Incomplete Multi-view Learning under Label Shift (IMLLS). In this framework, we first give the formal definitions of IMLLS and the bidirectional complete representation which describes the intrinsic and common structure. Then, a multilayer perceptron which combines the reconstruction and classification loss is employed to learn the latent representation, whose existence, consistency and universality are proved with the theoretical satisfaction of label shift assumption. After that, to align the label distribution, the learned representation and trained source classifier are used to estimate the importance weight by designing a new estimation scheme which balances the error generated by finite samples in theory. Finally, the trained classifier reweighted by the estimated weight is fine-tuned to reduce the gap between the source and target representations. Extensive experimental results validate the effectiveness of our algorithm over existing state-of-the-arts methods in various aspects, together with its effectiveness in discriminating schizophrenic patients from healthy controls.