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Searching for minimal optimal neural networks

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  • Ho, Lam Si Tung
  • Dinh, Vu

Abstract

Large neural network models have high predictive power but may suffer from overfitting if the training set is not large enough. Therefore, it is desirable to select an appropriate size for neural networks. The destructive approach, which starts with a large architecture and then reduces the size using a Lasso-type penalty, has been used extensively for this task. Despite its popularity, there is no theoretical guarantee for this technique. Based on the notion of minimal neural networks, we posit a rigorous mathematical framework for studying the asymptotic theory of the destructive technique. We prove that Adaptive group Lasso is consistent and can reconstruct the correct number of hidden nodes of one-hidden-layer feedforward networks with high probability. To the best of our knowledge, this is the first theoretical result establishing for the destructive technique.

Suggested Citation

  • Ho, Lam Si Tung & Dinh, Vu, 2022. "Searching for minimal optimal neural networks," Statistics & Probability Letters, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:stapro:v:183:y:2022:i:c:s0167715221002947
    DOI: 10.1016/j.spl.2021.109353
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    References listed on IDEAS

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    1. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    2. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
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    Cited by:

    1. Do, Quan Huu & Nguyen, Binh T. & Ho, Lam Si Tung, 2024. "A generalization bound of deep neural networks for dependent data," Statistics & Probability Letters, Elsevier, vol. 208(C).

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