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Statistical guarantees for sparse deep learning

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  • Johannes Lederer

    (Ruhr-University Bochum)

Abstract

Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for sparse deep learning. In contrast to previous work, we consider different types of sparsity, such as few active connections, few active nodes, and other norm-based types of sparsity. Moreover, our theories cover important aspects that previous theories have neglected, such as multiple outputs, regularization, and $$\ell_{2}$$ ℓ 2 -loss. The guarantees have a mild dependence on network widths and depths, which means that they support the application of sparse but wide and deep networks from a statistical perspective. Some of the concepts and tools that we use in our derivations are uncommon in deep learning and, hence, might be of additional interest.

Suggested Citation

  • Johannes Lederer, 2024. "Statistical guarantees for sparse deep learning," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(2), pages 231-258, June.
    • Handle: RePEc:spr:alstar:v:108:y:2024:i:2:d:10.1007_s10182-022-00467-3
    DOI: 10.1007/s10182-022-00467-3
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    References listed on IDEAS

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    1. Arnak S. Dalalyan & Mohamed Hebiri & Johannes Lederer, 2014. "On the Prediction Performance of the Lasso," Working Papers 2014-05, Center for Research in Economics and Statistics.
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