Optimizing Partial Area Under the Top-k Curve: Theory and Practice

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.

Multi-Attention Network for Compressed Video Referring Object Segmentation

Referring video object segmentation aims to segment the object referred by a given language expression. Existing works typically require compressed video bitstream to be decoded to RGB frames before being segmented, which increases computation and storage requirements and ultimately slows the inference down. This may hamper its application in real-world computing resource limited scenarios, such as autonomous cars and drones. To alleviate this problem, in this paper, we explore the referring object segmentation task on compressed videos, namely on the original video data flow. Besides the inherent difficulty of the video referring object segmentation task itself, obtaining discriminative representation from compressed video is also rather challenging. To address this problem, we propose a multi-attention network which consists of dual-path dual-attention module and a query-based cross-modal Transformer module. Specifically, the dual-path dual-attention module is designed to extract effective representation from compressed data in three modalities, i.e., I-frame, Motion Vector and Residual. The query-based cross-modal Transformer firstly models the correlation between linguistic and visual modalities, and then the fused multi-modality features are used to guide object queries to generate a content-aware dynamic kernel and to predict final segmentation masks. Different from previous works, we propose to learn just one kernel, which thus removes the complicated post mask-matching procedure of existing methods. Extensive promising experimental results on three challenging datasets show the effectiveness of our method compared against several state-of-the-art methods which are proposed for processing RGB data. Source code is available at: https://github.com/DexiangHong/MANet.

Entity-enhanced Adaptive Reconstruction Network for Weakly Supervised Referring Expression Grounding

Weakly supervised Referring Expression Grounding (REG) aims to ground a particular target in an image described by a language expression while lacking the correspondence between target and expression. Two main problems exist in weakly supervised REG. First, the lack of region-level annotations introduces ambiguities between proposals and queries. Second, most previous weakly supervised REG methods ignore the discriminative location and context of the referent, causing difficulties in distinguishing the target from other same-category objects. To address the above challenges, we design an entity-enhanced adaptive reconstruction network (EARN). Specifically, EARN includes three modules: entity enhancement, adaptive grounding, and collaborative reconstruction. In entity enhancement, we calculate semantic similarity as supervision to select the candidate proposals. Adaptive grounding calculates the ranking score of candidate proposals upon subject, location and context with hierarchical attention. Collaborative reconstruction measures the ranking result from three perspectives: adaptive reconstruction, language reconstruction and attribute classification. The adaptive mechanism helps to alleviate the variance of different referring expressions. Experiments on five datasets show EARN outperforms existing state-of-the-art methods. Qualitative results demonstrate that the proposed EARN can better handle the situation where multiple objects of a particular category are situated together.

Meta-Wrapper: Differentiable Wrapping Operator for User Interest Selection in CTR Prediction

Click-through rate (CTR) prediction, whose goal is to predict the probability of the user to click on an item, has become increasingly significant in the recommender systems. Recently, some deep learning models with the ability to automatically extract the user interest from his/her behaviors have achieved great success. In these work, the attention mechanism is used to select the user interested items in historical behaviors, improving the performance of the CTR predictor. Normally, these attentive modules can be jointly trained with the base predictor by using gradient descents. In this paper, we regard user interest modeling as a feature selection problem, which we call user interest selection. For such a problem, we propose a novel approach under the framework of the wrapper method, which is named Meta-Wrapper. More specifically, we use a differentiable module as our wrapping operator and then recast its learning problem as a continuous bilevel optimization. Moreover, we use a meta-learning algorithm to solve the optimization and theoretically prove its convergence. Meanwhile, we also provide theoretical analysis to show that our proposed method 1) efficiencies the wrapper-based feature selection, and 2) achieves better resistance to overfitting. Finally, extensive experiments on three public datasets manifest the superiority of our method in boosting the performance of CTR prediction.

AdAUC: End-to-end Adversarial AUC Optimization Against Long-tail Problems

It is well-known that deep learning models are vulnerable to adversarial examples. Existing studies of adversarial training have made great progress against this challenge. As a typical trait, they often assume that the class distribution is overall balanced. However, long-tail datasets are ubiquitous in a wide spectrum of applications, where the amount of head class instances is larger than the tail classes. Under such a scenario, AUC is a much more reasonable metric than accuracy since it is insensitive toward class distribution. Motivated by this, we present an early trial to explore adversarial training methods to optimize AUC. The main challenge lies in that the positive and negative examples are tightly coupled in the objective function. As a direct result, one cannot generate adversarial examples without a full scan of the dataset. To address this issue, based on a concavity regularization scheme, we reformulate the AUC optimization problem as a saddle point problem, where the objective becomes an instance-wise function. This leads to an end-to-end training protocol. Furthermore, we provide a convergence guarantee of the proposed algorithm. Our analysis differs from the existing studies since the algorithm is asked to generate adversarial examples by calculating the gradient of a min-max problem. Finally, the extensive experimental results show the performance and robustness of our algorithm in three long-tail datasets.

Geometry Interaction Knowledge Graph Embeddings

Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved), hyperbolic space (negatively curved) or hyperspherical space (positively curved) to maintain their specific geometric structures (e.g., chain, hierarchy and ring structures). However, the topological structure of KGs appears to be complicated, since it may contain multiple types of geometric structures simultaneously. Therefore, embedding KGs in a single space, no matter the Euclidean space, hyperbolic space or hyperspheric space, cannot capture the complex structures of KGs accurately. To overcome this challenge, we propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Theoretically, our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities. Experimental results on three well-established knowledge graph completion benchmarks show that our GIE achieves the state-of-the-art performance with fewer parameters.

ER: Equivariance Regularizer for Knowledge Graph Completion

Tensor factorization and distanced based models play important roles in knowledge graph completion (KGC). However, the relational matrices in KGC methods often induce a high model complexity, bearing a high risk of overfitting. As a remedy, researchers propose a variety of different regularizers such as the tensor nuclear norm regularizer. Our motivation is based on the observation that the previous work only focuses on the "size" of the parametric space, while leaving the implicit semantic information widely untouched. To address this issue, we propose a new regularizer, namely, Equivariance Regularizer (ER), which can suppress overfitting by leveraging the implicit semantic information. Specifically, ER can enhance the generalization ability of the model by employing the semantic equivariance between the head and tail entities. Moreover, it is a generic solution for both distance based models and tensor factorization based models. The experimental results indicate a clear and substantial improvement over the state-of-the-art relation prediction methods.

Optimizing Two-way Partial AUC with an End-to-end Framework

The Area Under the ROC Curve (AUC) is a crucial metric for machine learning, which evaluates the average performance over all possible True Positive Rates (TPRs) and False Positive Rates (FPRs). Based on the knowledge that a skillful classifier should simultaneously embrace a high TPR and a low FPR, we turn to study a more general variant called Two-way Partial AUC (TPAUC), where only the region with $\mathsf{TPR} \ge \alpha, \mathsf{FPR} \le \beta$ is included in the area. Moreover, recent work shows that the TPAUC is essentially inconsistent with the existing Partial AUC metrics where only the FPR range is restricted, opening a new problem to seek solutions to leverage high TPAUC. Motivated by this, we present the first trial in this paper to optimize this new metric. The critical challenge along this course lies in the difficulty of performing gradient-based optimization with end-to-end stochastic training, even with a proper choice of surrogate loss. To address this issue, we propose a generic framework to construct surrogate optimization problems, which supports efficient end-to-end training with deep learning. Moreover, our theoretical analyses show that: 1) the objective function of the surrogate problems will achieve an upper bound of the original problem under mild conditions, and 2) optimizing the surrogate problems leads to good generalization performance in terms of TPAUC with a high probability. Finally, empirical studies over several benchmark datasets speak to the efficacy of our framework.

Rethinking Collaborative Metric Learning: Toward an Efficient Alternative without Negative Sampling

The recently proposed Collaborative Metric Learning (CML) paradigm has aroused wide interest in the area of recommendation systems (RS) owing to its simplicity and effectiveness. Typically, the existing literature of CML depends largely on the \textit{negative sampling} strategy to alleviate the time-consuming burden of pairwise computation. However, in this work, by taking a theoretical analysis, we find that negative sampling would lead to a biased estimation of the generalization error. Specifically, we show that the sampling-based CML would introduce a bias term in the generalization bound, which is quantified by the per-user \textit{Total Variance} (TV) between the distribution induced by negative sampling and the ground truth distribution. This suggests that optimizing the sampling-based CML loss function does not ensure a small generalization error even with sufficiently large training data. Moreover, we show that the bias term will vanish without the negative sampling strategy. Motivated by this, we propose an efficient alternative without negative sampling for CML named \textit{Sampling-Free Collaborative Metric Learning} (SFCML), to get rid of the sampling bias in a practical sense. Finally, comprehensive experiments over seven benchmark datasets speak to the superiority of the proposed algorithm.

Automatic Relation-aware Graph Network Proliferation

Graph neural architecture search has sparked much attention as Graph Neural Networks (GNNs) have shown powerful reasoning capability in many relational tasks. However, the currently used graph search space overemphasizes learning node features and neglects mining hierarchical relational information. Moreover, due to diverse mechanisms in the message passing, the graph search space is much larger than that of CNNs. This hinders the straightforward application of classical search strategies for exploring complicated graph search space. We propose Automatic Relation-aware Graph Network Proliferation (ARGNP) for efficiently searching GNNs with a relation-guided message passing mechanism. Specifically, we first devise a novel dual relation-aware graph search space that comprises both node and relation learning operations. These operations can extract hierarchical node/relational information and provide anisotropic guidance for message passing on a graph. Second, analogous to cell proliferation, we design a network proliferation search paradigm to progressively determine the GNN architectures by iteratively performing network division and differentiation. The experiments on six datasets for four graph learning tasks demonstrate that GNNs produced by our method are superior to the current state-of-the-art hand-crafted and search-based GNNs. Codes are available at https://github.com/phython96/ARGNP.