Scalable large margin pairwise learning algorithms

2019 Summer.Includes bibliographical references.Classification is a major task in machine learning and data mining applications. Many of these applications involve building a classification model using a large volume of imbalanced data. In such an imbalanced learning scenario, the area under the ROC curve (AUC) has proven to be a reliable performance measure to evaluate a classifier. Therefore, it is desirable to develop scalable learning algorithms that maximize the AUC metric directly. The kernelized AUC maximization machines have established a superior generalization ability compared to linear AUC machines. However, the computational cost of the kernelized machines hinders their scalability. To address this problem, we propose a large-scale nonlinear AUC maximization algorithm that learns a batch linear classifier on approximate feature space computed via the k-means Nyström method. The proposed algorithm is shown empirically to achieve comparable AUC classification performance or even better than the kernel AUC machines, while its training time is faster by several orders of magnitude. However, the computational complexity of the linear batch model compromises its scalability when training sizable datasets. Hence, we develop a second-order online AUC maximization algorithms based on a confidence-weighted model. The proposed algorithms exploit the second-order information to improve the convergence rate and implement a fixed-size buffer to address the multivariate nature of the AUC objective function. We also extend our online linear algorithms to consider an approximate feature map constructed using random Fourier features in an online setting. The results show that our proposed algorithms outperform or are at least comparable to the competing online AUC maximization methods. Despite their scalability, we notice that online first and second-order AUC maximization methods are prone to suboptimal convergence. This can be attributed to the limitation of the hypothesis space. A potential improvement can be attained by learning stochastic online variants. However, the vanilla stochastic methods also suffer from slow convergence because of the high variance introduced by the stochastic process. We address the problem of slow convergence by developing a fast convergence stochastic AUC maximization algorithm. The proposed stochastic algorithm is accelerated using a unique combination of scheduled regularization update and scheduled averaging. The experimental results show that the proposed algorithm performs better than the state-of-the-art online and stochastic AUC maximization methods in terms of AUC classification accuracy. Moreover, we develop a proximal variant of our accelerated stochastic AUC maximization algorithm. The proposed method applies the proximal operator to the hinge loss function. Therefore, it evaluates the gradient of the loss function at the approximated weight vector. Experiments on several benchmark datasets show that our proximal algorithm converges to the optimal solution faster than the previous AUC maximization algorithms

SPARSITY AND WEAK SUPERVISION IN QUANTUM MACHINE LEARNING

Quantum computing is an interdisciplinary field at the intersection of computer science, mathematics, and physics that studies information processing tasks on a quantum computer. A quantum computer is a device whose operations are governed by the laws of quantum mechanics. As building quantum computers is nearing the era of commercialization and quantum supremacy, it is essential to think of potential applications that we might benefit from. Among many applications of quantum computation, one of the emerging fields is quantum machine learning. We focus on predictive models for binary classification and variants of Support Vector Machines that we expect to be especially important when training data becomes so large that a quantum algorithm with a guaranteed speedup becomes useful. We present a quantum machine learning algorithm for training Sparse Support Vector Machine for problems with large datasets that require a sparse solution. We also present the first quantum semi-supervised algorithm, where we still have a large dataset, but only a small fraction is provided with labels. While the availability of data for training machine learning models is steadily increasing, oftentimes it is much easier to collect feature vectors to obtain the corresponding labels. Here, we present a quantum machine learning algorithm for training Semi-Supervised Kernel Support Vector Machines. The algorithm uses recent advances in quantum sample-based Hamiltonian simulation to extend the existing Quantum LS-SVM algorithm to handle the semi-supervised term in the loss while maintaining the same quantum speedup as the Quantum LS-SVM