本文为德国凯泽斯劳藤大学（作者：Kumar Shridhar）的硕士论文，共90页。

人工神经网络是一种互连系统，它通过学习实例来完成给定的任务，而不必事先了解该任务。这是通过为每个节点中的权重找到最佳点估计来完成的。一般来说，使用点估计作为权重的网络在大型数据集上表现良好，但它们无法在数据很少或没有数据的区域中表达不确定性，从而导致决策过于自信。

本文提出了一种基于变分推理的贝叶斯卷积神经网络（BayesCNN），它引入了权值上的概率分布。此外，所提出的BayesCNN结构也被应用于图像分类、图像超分辨率和生成对抗网络等任务中。BayesCNN是基于Backprop提出的贝叶斯模型，它导出了真后验概率的变分近似。我们提出的方法不仅在相同的架构中实现了与频率推断相当的性能，而且还包含了不确定性和规则化的测量，还进一步消除了在模型中使用的dropout。此外，我们还预测了模型预测是如何基于认知和偶然的不确定性，最后，我们提出了修剪贝叶斯架构的方法，使其更具计算效率。

论文的第一部分对贝叶斯神经网络进行了解释，并将其应用于图像分类任务中。分类结果与基于MNIST、CIFAR-10和CIFAR-100数据集的点估计架构进行了比较。此外，还计算了不确定性，对贝叶斯架构进行了修剪，并对结果进行了比较。在论文的第二部分中，该概念进一步应用于其他计算机视觉任务，即图像超分辨率和生成对抗网络。对贝叶斯神经网络的概念进行了测试，并与同类领域的其他概念进行了比较。

Artificial Neural Networks are connectionist systems that perform a given task by learning on examples without having prior knowledge about the task. This is done by finding an optimal point estimate for the weights in every node. Generally, the network using point estimates as weights perform well with large datasets, but they fail to express uncertainty in regions with little or no data, leading to overconfident decisions. In this thesis, Bayesian Convolutional Neural Network (BayesCNN) using Variational Inference is proposed, that introduces probability distribution over the weights. Furthermore, the proposed BayesCNN architecture is applied to tasks like Image Classification, Image Super-Resolution and Generative Adversarial Networks. BayesCNN is based on Bayes by Backprop which derives a variational approximation to the true posterior. Our proposed method not only achieves performances equivalent to frequentist inference in identical architectures but also incorporate a measurement for uncertainties and regularisation. It further eliminates the use of dropout in the model. Moreover, we predict how certain the model prediction is based on the epistemic and aleatoric uncertainties and finally, we propose ways to prune the Bayesian architecture and to make it more computational and time effective. In the first part of the thesis, the Bayesian Neural Network is explained and it is applied to an Image Classification task. The results are compared to point-estimates based architectures on MNIST, CIFAR-10, and CIFAR-100 datasets. Moreover, uncertainties are calculated and the architecture is pruned and a comparison between the results is drawn. In the second part of the thesis, the concept is further applied to other computer vision tasks namely, Image Super-Resolution and Generative Adversarial Networks. The concept of BayesCNN is tested and compared against other concepts in a similar domain.

1 引言

1.1 问题描述

1.2 当前研究概况

1.3 我们的假设

1.4 本文研究贡献

2 项目背景

2.1 神经网络

2.2 基于概率的机器学习

2.3 贝叶斯学习的不确定性

2.4 后向传播

2.5 模型权重修剪

3 相关研究工作

4 相关概念

4.1 变差推断的贝叶斯卷积神经网络

4.2 CNN中的不确定估计

4.3 模型修剪

5 经验分析

5.1 实验方法

5.2 案例1：小型数据集（MNIST、CIFAR-10）

5.3 案例2：大型数据集（CIFAR-100）

5.4 不确定估计

5.5 模型修剪

5.6 训练时间

6 应用

6.1 图像超分辨率的BayesCNN应用

6.2 生成对抗网络的BayesCNN应用

7 结论与未来研究展望

附录A 实验规范

附录B 如何重复实验结果 

完整原文下载地址：

http://page2.dfpan.com/fs/el0caj62c2e1e289166/ 

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