Improper Deep Kernels

Uri Heinemann
Roi Livni
Amir Globerson
Proceedings of The 19th International Conference on Artificial Intelligence and Statististics.(2016)
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Neural networks have recently re-emerged as a powerful hypothesis class, yielding impressive classification accuracy in multiple domains. However, their training is a non-convex optimization problem which poses theoretical and practical challenges. Here we address this difficulty by turning to ``improper'' learning of neural nets. In other words, we learn a classifier that is not a neural net but is competitive with the best neural net model given a sufficient number of training examples. Our approach relies on a novel kernel construction scheme in which the kernel is a result of integration over the set of all possible instantiation of neural models. It turns out that the corresponding integral can be evaluated in closed-form via a simple recursion. Thus we translate the non-convex, hard learning problem of a neural net to a SVM with an appropriate kernel. We also provide sample complexity results which depend on the stability of the optimal neural net.

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