In this paper, we study the problem of multitask metric learning (mtML). We first examine the generalization bound of the regularized mtML formulation based on the notion of algorithmic stability, proving the convergence rate of mtML and revealing the trade-off between the tasks. Moreover, we also establish the theoretical connection between the mtML, single-task learning and pooling-task learning approaches. In addition, we present a novel boosting-based mtML (mt-BML) algorithm, which scales well with the feature dimension of the data. Finally, we also devise an efficient second-order Riemannian retraction operator which is tailored specifically to our mt-BML algorithm. It produces a low-rank solution of mtML to reduce the model complexity, and may also improve generalization performances. Extensive evaluations on several benchmark data sets verify the effectiveness of our learning algorithm.

We present a novel multitask learning framework called multitask generalized eigenvalue program (MTGEP), which jointly solves multiple related generalized eigenvalue problems (GEPs). This framework is quite general and can be applied to many eigenvalue problems in machine learning and pattern recognition, ranging from supervised learning to unsupervised learning, such as principal component analysis (PCA), Fisher discriminant analysis (FDA), common spatial pattern (CSP), and so on. The core assumption of our approach is that the leading eigenvectors of related GEPs lie in some subspace that can be approximated by a sparse linear combination of basis vectors. As a result, these GEPs can be jointly solved by a sparse coding approach. Empirical evaluation with both synthetic and benchmark real world datasets validates the efficacy and efficiency of the proposed techniques, especially for grouped multitask GEPs.

While both cost-sensitive learning and online learning have been studied separately, these two issues have seldom been addressed simultaneously. Yet, there are many applications where both aspects are important. This paper investigates a class of algorithmic approaches suitable for online cost-sensitive learning, designed for such problems. The basic idea is to leverage existing methods for online ensemble algorithms, and combine these with batch mode methods for cost-sensitive bagging/boosting algorithms. Within this framework, we describe several theoretically sound online cost-sensitive bagging and online cost-sensitive boosting algorithms, and show that the convergence of the proposed algorithms is guaranteed under certain conditions. We then present extensive experimental results on benchmark datasets to compare the performance of the various proposed approaches.

The related problems of transfer learning and multitask learning have attracted significant attention, generating a rich literature of models and algorithms. Yet most existing approaches are studied in an offline fashion, implicitly assuming that data from different domains are given as a batch. Such an assumption is not valid in many real-world applications where data samples arrive sequentially, and one wants a good learner even from few examples. The goal of our work is to provide sound extensions to existing transfer and multitask learning algorithms such that they can be used in an anytime setting. More specifically, we propose two novel online boosting algorithms, one for transfer learning and one for multitask learning, both designed to leverage the knowledge of instances in other domains. The experimental results show state-of-the-art empirical performance on standard benchmarks, and we present results of using our methods for effectively detecting new seizures in patients with epilepsy from very few previous samples.