Misclassification bounds for PAC-Bayesian sparse deep learning
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916578453356544 |
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| author | Mai, The Tien |
| author_facet | Mai, The Tien |
| contents | Recently, there has been a significant focus on exploring the theoretical aspects of deep learning, especially regarding its performance in classification tasks. Bayesian deep learning has emerged as a unified probabilistic framework, seeking to integrate deep learning with Bayesian methodologies seamlessly. However, there exists a gap in the theoretical understanding of Bayesian approaches in deep learning for classification. This study presents an attempt to bridge that gap. By leveraging PAC-Bayes bounds techniques, we present theoretical results on the prediction or misclassification error of a probabilistic approach utilizing Spike-and-Slab priors for sparse deep learning in classification. We establish non-asymptotic results for the prediction error. Additionally, we demonstrate that, by considering different architectures, our results can achieve minimax optimal rates in both low and high-dimensional settings, up to a logarithmic factor. Moreover, our additional logarithmic term yields slight improvements over previous works. Additionally, we propose and analyze an automated model selection approach aimed at optimally choosing a network architecture with guaranteed optimality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Misclassification bounds for PAC-Bayesian sparse deep learning Mai, The Tien Statistics Theory Machine Learning Recently, there has been a significant focus on exploring the theoretical aspects of deep learning, especially regarding its performance in classification tasks. Bayesian deep learning has emerged as a unified probabilistic framework, seeking to integrate deep learning with Bayesian methodologies seamlessly. However, there exists a gap in the theoretical understanding of Bayesian approaches in deep learning for classification. This study presents an attempt to bridge that gap. By leveraging PAC-Bayes bounds techniques, we present theoretical results on the prediction or misclassification error of a probabilistic approach utilizing Spike-and-Slab priors for sparse deep learning in classification. We establish non-asymptotic results for the prediction error. Additionally, we demonstrate that, by considering different architectures, our results can achieve minimax optimal rates in both low and high-dimensional settings, up to a logarithmic factor. Moreover, our additional logarithmic term yields slight improvements over previous works. Additionally, we propose and analyze an automated model selection approach aimed at optimally choosing a network architecture with guaranteed optimality. |
| title | Misclassification bounds for PAC-Bayesian sparse deep learning |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2405.01304 |