8,103 research outputs found
Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review
The paper characterizes classes of functions for which deep learning can be
exponentially better than shallow learning. Deep convolutional networks are a
special case of these conditions, though weight sharing is not the main reason
for their exponential advantage
Random Feature Maps for Dot Product Kernels
Approximating non-linear kernels using feature maps has gained a lot of
interest in recent years due to applications in reducing training and testing
times of SVM classifiers and other kernel based learning algorithms. We extend
this line of work and present low distortion embeddings for dot product kernels
into linear Euclidean spaces. We base our results on a classical result in
harmonic analysis characterizing all dot product kernels and use it to define
randomized feature maps into explicit low dimensional Euclidean spaces in which
the native dot product provides an approximation to the dot product kernel with
high confidence.Comment: To appear in the proceedings of the 15th International Conference on
Artificial Intelligence and Statistics (AISTATS 2012). This version corrects
a minor error with Lemma 10. Acknowledgements : Devanshu Bhimwa
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