Generalization bounds for deep thresholding networks
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We consider compressive sensing in the scenario where the sparsity basis (dictionary) is not known in advance, but needs to be learned from examples. Motivated by the well-known iterative soft thresholding algorithm for the reconstruction, we define deep networks parametrized by the dictionary, which we call deep thresholding networks. Based on training samples, we aim at learning the optimal sparsifying dictionary and thereby the optimal network that reconstructs signals from their low-dimensional linear measurements. The dictionary learning is performed via minimizing the empirical risk. We derive generalization bounds by analyzing the Rademacher complexity of hypothesis classes consisting of such deep networks. We obtain estimates of the sample complexity that depend only linearly on the dimensions and on the depth.
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