The Area Under the ROC Curve (AUC) is a widely employed metric in long-tailed classification scenarios. Nevertheless, most existing methods primarily assume that training and testing examples are drawn i.i.d. from the same distribution, which is often unachievable in practice. Distributionally Robust Optimization (DRO) enhances model performance by optimizing it for the local worst-case scenario, but directly integrating AUC optimization with DRO results in an intractable optimization problem. To tackle this challenge, methodically we propose an instance-wise surrogate loss of Distributionally Robust AUC (DRAUC) and build our optimization framework on top of it. Moreover, we highlight that conventional DRAUC may induce label bias, hence introducing distribution-aware DRAUC as a more suitable metric for robust AUC learning. Theoretically, we affirm that the generalization gap between the training loss and testing error diminishes if the training set is sufficiently large. Empirically, experiments on corrupted benchmark datasets demonstrate the effectiveness of our proposed method. Code is available at: https://github.com/EldercatSAM/DRAUC.
Neural Collapse (NC) is a well-known phenomenon of deep neural networks in the terminal phase of training (TPT). It is characterized by the collapse of features and classifier into a symmetrical structure, known as simplex equiangular tight frame (ETF). While there have been extensive studies on optimization characteristics showing the global optimality of neural collapse, little research has been done on the generalization behaviors during the occurrence of NC. Particularly, the important phenomenon of generalization improvement during TPT has been remaining in an empirical observation and lacking rigorous theoretical explanation. In this paper, we establish the connection between the minimization of CE and a multi-class SVM during TPT, and then derive a multi-class margin generalization bound, which provides a theoretical explanation for why continuing training can still lead to accuracy improvement on test set, even after the train accuracy has reached 100%. Additionally, our further theoretical results indicate that different alignment between labels and features in a simplex ETF can result in varying degrees of generalization improvement, despite all models reaching NC and demonstrating similar optimization performance on train set. We refer to this newly discovered property as "non-conservative generalization". In experiments, we also provide empirical observations to verify the indications suggested by our theoretical results.
Real-world datasets are typically imbalanced in the sense that only a few classes have numerous samples, while many classes are associated with only a few samples. As a result, a na\"ive ERM learning process will be biased towards the majority classes, making it difficult to generalize to the minority classes. To address this issue, one simple but effective approach is to modify the loss function to emphasize the learning on minority classes, such as re-weighting the losses or adjusting the logits via class-dependent terms. However, existing generalization analysis of such losses is still coarse-grained and fragmented, failing to explain some empirical results. To bridge this gap, we propose a novel technique named data-dependent contraction to capture how these modified losses handle different classes. On top of this technique, a fine-grained generalization bound is established for imbalanced learning, which helps reveal the mystery of re-weighting and logit-adjustment in a unified manner. Furthermore, a principled learning algorithm is developed based on the theoretical insights. Finally, the empirical results on benchmark datasets not only validate the theoretical results but also demonstrate the effectiveness of the proposed method.
We proposed an easy method of Zero-Shot semantic segmentation by using style transfer. In this case, we successfully used a medical imaging dataset (Blood Cell Imagery) to train a model for river ice semantic segmentation. First, we built a river ice semantic segmentation dataset IPC_RI_SEG using a fixed camera and covering the entire ice melting process of the river. Second, a high-resolution texture fusion semantic segmentation network named IceHrNet is proposed. The network used HRNet as the backbone and added ASPP and Decoder segmentation heads to retain low-level texture features for fine semantic segmentation. Finally, a simple and effective advanced style transfer learning strategy was proposed, which can perform zero-shot transfer learning based on cross-domain semantic segmentation datasets, achieving a practical effect of 87% mIoU for semantic segmentation of river ice without target training dataset (25% mIoU for None Stylized, 65% mIoU for Conventional Stylized, our strategy improved by 22%). Experiments showed that the IceHrNet outperformed the state-of-the-art methods on the texture-focused dataset IPC_RI_SEG, and achieved an excellent result on the shape-focused river ice datasets. In zero-shot transfer learning, IceHrNet achieved an increase of 2 percentage points compared to other methods. Our code and model are published on https://github.com/PL23K/IceHrNet.
In this paper, we extends original Neural Collapse Phenomenon by proving Generalized Neural Collapse hypothesis. We obtain Grassmannian Frame structure from the optimization and generalization of classification. This structure maximally separates features of every two classes on a sphere and does not require a larger feature dimension than the number of classes. Out of curiosity about the symmetry of Grassmannian Frame, we conduct experiments to explore if models with different Grassmannian Frames have different performance. As a result, we discover the Symmetric Generalization phenomenon. We provide a theorem to explain Symmetric Generalization of permutation. However, the question of why different directions of features can lead to such different generalization is still open for future investigation.
The Partial Area Under the ROC Curve (PAUC), typically including One-way Partial AUC (OPAUC) and Two-way Partial AUC (TPAUC), measures the average performance of a binary classifier within a specific false positive rate and/or true positive rate interval, which is a widely adopted measure when decision constraints must be considered. Consequently, PAUC optimization has naturally attracted increasing attention in the machine learning community within the last few years. Nonetheless, most of the existing methods could only optimize PAUC approximately, leading to inevitable biases that are not controllable. Fortunately, a recent work presents an unbiased formulation of the PAUC optimization problem via distributional robust optimization. However, it is based on the pair-wise formulation of AUC, which suffers from the limited scalability w.r.t. sample size and a slow convergence rate, especially for TPAUC. To address this issue, we present a simpler reformulation of the problem in an asymptotically unbiased and instance-wise manner. For both OPAUC and TPAUC, we come to a nonconvex strongly concave minimax regularized problem of instance-wise functions. On top of this, we employ an efficient solver enjoys a linear per-iteration computational complexity w.r.t. the sample size and a time-complexity of $O(\epsilon^{-1/3})$ to reach a $\epsilon$ stationary point. Furthermore, we find that the minimax reformulation also facilitates the theoretical analysis of generalization error as a byproduct. Compared with the existing results, we present new error bounds that are much easier to prove and could deal with hypotheses with real-valued outputs. Finally, extensive experiments on several benchmark datasets demonstrate the effectiveness of our method.
Collaborative Metric Learning (CML) has recently emerged as a popular method in recommendation systems (RS), closing the gap between metric learning and Collaborative Filtering. Following the convention of RS, existing methods exploit unique user representation in their model design. This paper focuses on a challenging scenario where a user has multiple categories of interests. Under this setting, we argue that the unique user representation might induce preference bias, especially when the item category distribution is imbalanced. To address this issue, we propose a novel method called \textit{Diversity-Promoting Collaborative Metric Learning} (DPCML), with the hope of considering the commonly ignored minority interest of the user. The key idea behind DPCML is to include a multiple set of representations for each user in the system. Based on this embedding paradigm, user preference toward an item is aggregated from different embeddings by taking the minimum item-user distance among the user embedding set. Furthermore, we observe that the diversity of the embeddings for the same user also plays an essential role in the model. To this end, we propose a \textit{diversity control regularization} term to accommodate the multi-vector representation strategy better. Theoretically, we show that DPCML could generalize well to unseen test data by tackling the challenge of the annoying operation that comes from the minimum value. Experiments over a range of benchmark datasets speak to the efficacy of DPCML.
Stochastic optimization of the Area Under the Precision-Recall Curve (AUPRC) is a crucial problem for machine learning. Although various algorithms have been extensively studied for AUPRC optimization, the generalization is only guaranteed in the multi-query case. In this work, we present the first trial in the single-query generalization of stochastic AUPRC optimization. For sharper generalization bounds, we focus on algorithm-dependent generalization. There are both algorithmic and theoretical obstacles to our destination. From an algorithmic perspective, we notice that the majority of existing stochastic estimators are biased only when the sampling strategy is biased, and is leave-one-out unstable due to the non-decomposability. To address these issues, we propose a sampling-rate-invariant unbiased stochastic estimator with superior stability. On top of this, the AUPRC optimization is formulated as a composition optimization problem, and a stochastic algorithm is proposed to solve this problem. From a theoretical perspective, standard techniques of the algorithm-dependent generalization analysis cannot be directly applied to such a listwise compositional optimization problem. To fill this gap, we extend the model stability from instancewise losses to listwise losses and bridge the corresponding generalization and stability. Additionally, we construct state transition matrices to describe the recurrence of the stability, and simplify calculations by matrix spectrum. Practically, experimental results on three image retrieval datasets on speak to the effectiveness and soundness of our framework.
In recent years, great progress has been made to incorporate unlabeled data to overcome the inefficiently supervised problem via semi-supervised learning (SSL). Most state-of-the-art models are based on the idea of pursuing consistent model predictions over unlabeled data toward the input noise, which is called consistency regularization. Nonetheless, there is a lack of theoretical insights into the reason behind its success. To bridge the gap between theoretical and practical results, we propose a worst-case consistency regularization technique for SSL in this paper. Specifically, we first present a generalization bound for SSL consisting of the empirical loss terms observed on labeled and unlabeled training data separately. Motivated by this bound, we derive an SSL objective that minimizes the largest inconsistency between an original unlabeled sample and its multiple augmented variants. We then provide a simple but effective algorithm to solve the proposed minimax problem, and theoretically prove that it converges to a stationary point. Experiments on five popular benchmark datasets validate the effectiveness of our proposed method.
Top-k error has become a popular metric for large-scale classification benchmarks due to the inevitable semantic ambiguity among classes. Existing literature on top-k optimization generally focuses on the optimization method of the top-k objective, while ignoring the limitations of the metric itself. In this paper, we point out that the top-k objective lacks enough discrimination such that the induced predictions may give a totally irrelevant label a top rank. To fix this issue, we develop a novel metric named partial Area Under the top-k Curve (AUTKC). Theoretical analysis shows that AUTKC has a better discrimination ability, and its Bayes optimal score function could give a correct top-K ranking with respect to the conditional probability. This shows that AUTKC does not allow irrelevant labels to appear in the top list. Furthermore, we present an empirical surrogate risk minimization framework to optimize the proposed metric. Theoretically, we present (1) a sufficient condition for Fisher consistency of the Bayes optimal score function; (2) a generalization upper bound which is insensitive to the number of classes under a simple hyperparameter setting. Finally, the experimental results on four benchmark datasets validate the effectiveness of our proposed framework.