Bipartite ranking is a fundamental machine learning and data mining problem. It commonly concerns the maximization of the AUC metric. Recently, a number of studies have proposed online bipartite ranking algorithms to learn from massive streams of class-imbalanced data. These methods suggest both linear and kernel-based bipartite rank- ing algorithms based on first and second-order online learning. Unlike kernelized ranker, linear ranker is more scalable learning algorithm. The existing linear online bipartite ranking algorithms lack either handling non-separable data or constructing adaptive large margin. These limitations yield unreliable bipartite ranking performance. In this work, we propose a linear online confidence-weighted bipartite ranking algorithm (CBR) that adopts soft confidence-weighted learning. The proposed algorithm leverages the same properties of soft confidence-weighted learning in a framework for bipartite ranking. We also develop a diagonal variation of the proposed confidence-weighted bipartite ranking algorithm to deal with high-dimensional data by maintaining only the diagonal elements of the covariance matrix. We empirically evaluate the effectiveness of the proposed algorithms on several benchmark and high-dimensional datasets. The experimental results validate the reliability of the pro- posed algorithms. The results also show that our algorithms outperform or are at least comparable to the competing online AUC maximization methods.
@cite_37: Learning for maximizing AUC performance is an important research problem in machine learning. Unlike traditional batch learning methods for maximizing AUC which often suffer from poor scalability, recent years have witnessed some emerging studies that attempt to maximize AUC by single-pass online learning approaches. Despite their encouraging results reported, the existing online AUC maximization algorithms often adopt simple stochastic gradient descent approaches, which fail to exploit the geometry knowledge of the data observed in the online learning process, and thus could suffer from relatively slow convergence. To overcome the limitation of the existing studies, in this paper, we propose a novel algorithm of Adaptive Online AUC Maximization (AdaOAM), by applying an adaptive gradient method for exploiting the knowledge of historical gradients to perform more informative online learning. The new adaptive updating strategy by AdaOAM is less sensitive to parameter settings due to its natural effect of tuning the learning rate. In addition, the time complexity of the new algorithm remains the same as the previous non-adaptive algorithms. To demonstrate the effectiveness of the proposed algorithm, we analyze its theoretical bound, and further evaluate its empirical performance on both public benchmark datasets and anomaly detection datasets. The encouraging empirical results clearly show the effectiveness and efficiency of the proposed algorithm.
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@cite_2: Most studies of online learning measure the performance of a learner by classification accuracy, which is inappropriate for applications where the data are unevenly distributed among different classes. We address this limitation by developing online learning algorithm for maximizing Area Under the ROC curve (AUC), a metric that is widely used for measuring the classification performance for imbalanced data distributions. The key challenge of online AUC maximization is that it needs to optimize the pairwise loss between two instances from different classes. This is in contrast to the classical setup of online learning where the overall loss is a sum of losses over individual training examples. We address this challenge by exploiting the reservoir sampling technique, and present two algorithms for online AUC maximization with theoretic performance guarantee. Extensive experimental studies confirm the effectiveness and the efficiency of the proposed algorithms for maximizing AUC.
@cite_34: In this paper, we study the generalization properties of online learning based stochastic methods for supervised learning problems where the loss function is dependent on more than one training sample (e.g., metric learning, ranking). We present a generic decoupling technique that enables us to provide Rademacher complexity-based generalization error bounds. Our bounds are in general tighter than those obtained by (2012) for the same problem. Using our decoupling technique, we are further able to obtain fast convergence rates for strongly convex pairwise loss functions. We are also able to analyze a class of memory efficient online learning algorithms for pairwise learning problems that use only a bounded subset of past training samples to update the hypothesis at each step. Finally, in order to complement our generalization bounds, we propose a novel memory efficient online learning algorithm for higher order learning problems with bounded regret guarantees.
@cite_10: A major challenge in Content-Based Image Retrieval (CBIR) is to bridge the semantic gap between low-level image contents and high-level semantic concepts. Although researchers have investigated a variety of retrieval techniques using different types of features and distance functions, no single best retrieval solution can fully tackle this challenge. In a real-world CBIR task, it is often highly desired to combine multiple types of different feature representations and diverse distance measures in order to close the semantic gap. In this paper, we investigate a new framework of learning to rank for CBIR, which aims to seek the optimal combination of different retrieval schemes by learning from large-scale training data in CBIR. We first formulate the problem formally as a learning to rank task, which can be solved in general by applying the existing batch learning to rank algorithms from text information retrieval (IR). To further address the scalability towards large-scale online CBIR applications, we present a family of online learning to rank algorithms, which are significantly more efficient and scalable than classical batch algorithms for large-scale online CBIR. Finally, we conduct an extensive set of experiments, in which encouraging results show that our technique is effective, scalable and promising for large-scale CBIR.
@cite_17: In this paper, we propose a new Soft Confidence-Weighted (SCW) online learning scheme, which enables the conventional confidence-weighted learning method to handle non-separable cases. Unlike the previous confidence-weighted learning algorithms, the proposed soft confidence-weighted learning method enjoys all the four salient properties: (i) large margin training, (ii) confidence weighting, (iii) capability to handle non-separable data, and (iv) adaptive margin. Our experimental results show that the proposed SCW algorithms significantly outperform the original CW algorithm. When comparing with a variety of state-of-the-art algorithms (including AROW, NAROW and NHERD), we found that SCW generally achieves better or at least comparable predictive accuracy, but enjoys significant advantage of computational efficiency (i.e., smaller number of updates and lower time cost).
Our proposed method follows the online framework that maintains fixed-sized buffers to store instances from each class label. Further, it exploits the online second-order method @cite_17 to learn a robust bipartite ranking function. This distinguishes the proposed method from @cite_34 @cite_2 employing first-order online learning. Also, the proposed method is different from @cite_37 @cite_4 by learning a confidence-weighted ranker capable of dealing with non-separable data and learning an adaptive large margin. The most similar approaches to our method are @cite_10 @cite_11 . However, these are not designed to directly maximize the AUC. They also use classical first-order and second-order online learning whereas we use the soft variation of confidence-weighted learning that has shown a robust performance in the classification task @cite_17 .