Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Regularized multi--task learning
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Learning Multiple Tasks with Kernel Methods
The Journal of Machine Learning Research
Matrix Nearness Problems with Bregman Divergences
SIAM Journal on Matrix Analysis and Applications
Integrating low-rank and group-sparse structures for robust multi-task learning
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
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Multi-task learning (MTL) has drawn a lot of attentions in machine learning. By training multiple tasks simultaneously, information can be better shared across tasks. This leads to significant performance improvement in many problems. However, most existing methods assume that all tasks are related or their relationship follows a simple and specified structure. In this paper, we propose a novel manifold regularized framework for multi-task learning. Instead of assuming simple relationship among tasks, we propose to learn task decision functions as well as a manifold structure from data simultaneously. As manifold could be arbitrarily complex, we show that our proposed framework can contain many recent MTL models, e.g. RegMTL and cCMTL, as special cases. The framework can be solved by alternatively learning all tasks and the manifold structure. In particular, learning all tasks with the manifold regularization can be solved as a single-task learning problem, while the manifold structure can be obtained by successive Bregman projection on a convex feasible set. On both synthetic and real datasets, we show that our method can outperform the other competitive methods.