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multi_task_learning

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Multi-task feature learning

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### Multi-task feature learning

This is a method for learning multiple tasks simultaneously, assuming that they share a set of common latent features. It is based on regularizing the spectrum of the matrix of tasks. Regularization with the trace norm is a special case of this framework. Among the diverse applications of multi-task learning, one example is the personalized recommendation of products to consumers.

The methodology is presented in detail in the papers
[Multi-Task Feature Learning](http://ttic.uchicago.edu/~argyriou/papers/nips06_online.pdf),
[Convex Multi-Task Feature Learning](http://ttic.uchicago.edu/~argyriou/papers/mtl_feat.pdf)
and 
[A Spectral Regularization Framework for Multi-Task Structure Learning](http://ttic.uchicago.edu/~argyriou/papers/spectral_mtl.pdf).

Note that it is possible to use the method with a nonlinear kernel instead of explicit features. It suffices to run the code on the Gram matrix after a preprocessing with a Gram-Schmidt or Cholesky decomposition (see [Convex Multi-Task Feature Learning](http://ttic.uchicago.edu/~argyriou/papers/mtl_feat.pdf) sec. 5).

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