Random Feature-based Online Multi-kernel Learning in Environments with Unknown Dynamics

Kernel-based methods exhibit well-documented performance in various nonlinear learning tasks. Most of them rely on a preselected kernel, whose prudent choice presumes task-specific prior information. Especially when the latter is not available, multi-kernel learning has gained popularity thanks to its flexibility in choosing kernels from a prescribed kernel dictionary. Leveraging the random feature approximation and its recent orthogonality-promoting variant, the present contribution develops a scalable multi-kernel learning scheme (termed Raker) to obtain the sought nonlinear learning function `on the fly,' first for static environments. To further boost performance in dynamic environments, an adaptive multi-kernel learning scheme (termed AdaRaker) is developed. AdaRaker accounts not only for data-driven learning of kernel combination, but also for the unknown dynamics. Performance is analyzed in terms of both static and dynamic regrets. AdaRaker is uniquely capable of tracking nonlinear learning functions in environments with unknown dynamics, and with with analytic performance guarantees. Tests with synthetic and real datasets are carried out to showcase the effectiveness of the novel algorithms.Comment: 36 page

A Divide-and-Conquer Solver for Kernel Support Vector Machines

The kernel support vector machine (SVM) is one of the most widely used classification methods; however, the amount of computation required becomes the bottleneck when facing millions of samples. In this paper, we propose and analyze a novel divide-and-conquer solver for kernel SVMs (DC-SVM). In the division step, we partition the kernel SVM problem into smaller subproblems by clustering the data, so that each subproblem can be solved independently and efficiently. We show theoretically that the support vectors identified by the subproblem solution are likely to be support vectors of the entire kernel SVM problem, provided that the problem is partitioned appropriately by kernel clustering. In the conquer step, the local solutions from the subproblems are used to initialize a global coordinate descent solver, which converges quickly as suggested by our analysis. By extending this idea, we develop a multilevel Divide-and-Conquer SVM algorithm with adaptive clustering and early prediction strategy, which outperforms state-of-the-art methods in terms of training speed, testing accuracy, and memory usage. As an example, on the covtype dataset with half-a-million samples, DC-SVM is 7 times faster than LIBSVM in obtaining the exact SVM solution (to within $10^{-6}$ relative error) which achieves 96.15% prediction accuracy. Moreover, with our proposed early prediction strategy, DC-SVM achieves about 96% accuracy in only 12 minutes, which is more than 100 times faster than LIBSVM

Speaker verification using sequence discriminant support vector machines

This paper presents a text-independent speaker verification system using support vector machines (SVMs) with score-space kernels. Score-space kernels generalize Fisher kernels and are based on underlying generative models such as Gaussian mixture models (GMMs). This approach provides direct discrimination between whole sequences, in contrast with the frame-level approaches at the heart of most current systems. The resultant SVMs have a very high dimensionality since it is related to the number of parameters in the underlying generative model. To address problems that arise in the resultant optimization we introduce a technique called spherical normalization that preconditions the Hessian matrix. We have performed speaker verification experiments using the PolyVar database. The SVM system presented here reduces the relative error rates by 34% compared to a GMM likelihood ratio system