Learning for maximizing AUC performance is an important research problem in Machine Learning and Artificial Intelligence. 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 online gradient descent approaches that fail to exploit the geometrical knowledge of the data observed during the online learning process, and thus could suffer from relatively larger regret. To address the above limitation, in this work, we explore a novel algorithm of Adaptive Online AUC Maximization (AdaOAM) which employs an adaptive gradient method that exploits the knowledge of historical gradients to perform more informative online learning. The new adaptive updating strategy of the AdaOAM is less sensitive to the parameter settings and maintains the same time complexity as previous non-adaptive counterparts. Additionally, we extend the algorithm to handle high-dimensional sparse data (SAdaOAM) and address sparsity in the solution by performing lazy gradient updating. We analyze the theoretical bounds and evaluate their empirical performance on various types of data sets. The encouraging empirical results obtained clearly highlighted the effectiveness and efficiency of the proposed algorithms.
In most kernel based online learning algorithms, when an incoming instance is misclassified, it will be added into the pool of support vectors and assigned with a weight, which often remains unchanged during the rest of the learning process. This is clearly insufficient since when a new support vector is added, we generally expect the weights of the other existing support vectors to be updated in order to reflect the influence of the added support vector. In this paper, we propose a new online learning method, termed Double Updating Online Learning, or DUOL for short, that explicitly addresses this problem. Instead of only assigning a fixed weight to the misclassified example received at the current trial, the proposed online learning algorithm also tries to update the weight for one of the existing support vectors. We show that the mistake bound can be improved by the proposed online learning method. We conduct an extensive set of empirical evaluations for both binary and multi-class online learning tasks. The experimental results show that the proposed technique is considerably more effective than the state-of-the-art online learning algorithms. The source code is available to public at http: www.cais.ntu.edu.sg chhoi DUOL .    Malicious Uniform Resource Locator (URL) detection is an important problem in web search and mining, which plays a critical role in internet security. In literature, many existing studies have attempted to formulate the problem as a regular supervised binary classification task, which typically aims to optimize the prediction accuracy. However, in a real-world malicious URL detection task, the ratio between the number of malicious URLs and legitimate URLs is highly imbalanced, making it very inappropriate for simply optimizing the prediction accuracy. Besides, another key limitation of the existing work is to assume a large amount of training data is available, which is impractical as the human labeling cost could be potentially quite expensive. To solve these issues, in this paper, we present a novel framework of Cost-Sensitive Online Active Learning (CSOAL), which only queries a small fraction of training data for labeling and directly optimizes two cost-sensitive measures to address the class-imbalance issue. In particular, we propose two CSOAL algorithms and analyze their theoretical performance in terms of cost-sensitive bounds. We conduct an extensive set of experiments to examine the empirical performance of the proposed algorithms for a large-scale challenging malicious URL detection task, in which the encouraging results showed that the proposed technique by querying an extremely small-sized labeled data (about 0.5 out of 1-million instances) can achieve better or highly comparable classification performance in comparison to the state-of-the-art cost-insensitive and cost-sensitive online classification algorithms using a huge amount of labeled data. 1. Introduction 2. Prediction with expert advice 3. Tight bounds for specific losses 4. Randomized prediction 5. Efficient forecasters for large classes of experts 6. Prediction with limited feedback 7. Prediction and playing games 8. Absolute loss 9. Logarithmic loss 10. Sequential investment 11. Linear pattern recognition 12. Linear classification 13. Appendix. Although both cost-sensitive classification and online learning have been well studied separately in data mining and machine learning, there was very few comprehensive study of cost-sensitive online classification in literature. In this paper, we formally investigate this problem by directly optimizing cost-sensitive measures for an online classification task. As the first comprehensive study, we propose the Cost-Sensitive Double Updating Online Learning (CSDUOL) algorithms, which explores a recent double updating technique to tackle the online optimization task of cost-sensitive classification by maximizing the weighted sum or minimizing the weighted misclassification cost. We theoretically analyze the cost-sensitive measure bounds of the proposed algorithms, extensively examine their empirical performance for cost-sensitive online classification tasks, and finally demonstrate the application of our technique to solve online anomaly detection tasks.  We present AROW, an online learning algorithm for binary and multiclass problems that combines large margin training, confidence weighting, and the capacity to handle non-separable data. AROW performs adaptive regularization of the prediction function upon seeing each new instance, allowing it to perform especially well in the presence of label noise. We derive mistake bounds for the binary and multiclass settings that are similar in form to the second order perceptron bound. Our bounds do not assume separability. We also relate our algorithm to recent confidence-weighted online learning techniques. Empirical evaluations show that AROW achieves state-of-the-art performance on a wide range of binary and multiclass tasks, as well as robustness in the face of non-separable data.  In this paper, we propose a novel machine learning framework called "Online Transfer Learning" (OTL), which aims to attack an online learning task on a target domain by transferring knowledge from some source domain. We do not assume data in the target domain follows the same distribution as that in the source domain, and the motivation of our work is to enhance a supervised online learning task on a target domain by exploiting the existing knowledge that had been learnt from training data in source domains. OTL is in general very challenging since data in both source and target domains not only can be different in their class distributions, but also can be diverse in their feature representations. As a first attempt to this new research problem, we investigate two different settings of OTL: (i) OTL on homogeneous domains of common feature space, and (ii) OTL across heterogeneous domains of different feature spaces. For each setting, we propose effective OTL algorithms to solve online classification tasks, and show some theoretical bounds of the algorithms. In addition, we also apply the OTL technique to attack the challenging online learning tasks with concept-drifting data streams. Finally, we conduct extensive empirical studies on a comprehensive testbed, in which encouraging results validate the efficacy of our techniques.  