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Misclassification bounds for PAC-Bayesian sparse deep learning
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DOI：10.1007/s10994-024-06690-0.png)
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Abstract
En 中文
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.
Keywords:
Deep neural network
Binary classification
Prediction bounds
PAC-Bayes bounds
Fast rate
Sparse prior
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