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<p>This work presents a training methodology for Bayesian convolutional neural networks (BCNNs). The approach combines variational inference for the output layer with maximum likelihood estimation for remaining network parameters. The proposed variational Bayesian last layer model employs a Gaussian mixture as the variational posterior distribution over the last layer parameters (VBLL-GMM), enabling improved uncertainty representation. Unlike most variational methods that use Monte Carlo sampling to estimate the objective function, VBLL-GMM utilizes a deterministic lower bound on the evidence lower bound function. This maintains computational efficiency comparable to standard deterministic networks. Extensive experiments demonstrate the VBLL-GMM’s competitive performance compared to established probabilistic techniques in terms of accuracy, calibration, and out-of-distribution detection on diverse benchmark datasets.</p>

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Variational Bayesian Gaussian Mixture Last Layer of Convolutional Neural Network

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Mostafa Bakhouya,
  • Khalid Elghazi,
  • Hassan Ramchoun,
  • Mohammed Hadda,
  • Tawfik Masrour

摘要

This work presents a training methodology for Bayesian convolutional neural networks (BCNNs). The approach combines variational inference for the output layer with maximum likelihood estimation for remaining network parameters. The proposed variational Bayesian last layer model employs a Gaussian mixture as the variational posterior distribution over the last layer parameters (VBLL-GMM), enabling improved uncertainty representation. Unlike most variational methods that use Monte Carlo sampling to estimate the objective function, VBLL-GMM utilizes a deterministic lower bound on the evidence lower bound function. This maintains computational efficiency comparable to standard deterministic networks. Extensive experiments demonstrate the VBLL-GMM’s competitive performance compared to established probabilistic techniques in terms of accuracy, calibration, and out-of-distribution detection on diverse benchmark datasets.