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

人工神经网络是一种互联系统，它通过学习实例来执行给定的任务，而不必事先知道该任务。这是通过为每个节点中的权重找到一个最优点估计来实现的。一般来说，使用点估计作为权值的网络在处理大数据集时表现良好，但在数据很少或没有数据的区域，它们无法表达不确定性，从而导致过度自信决策。

本文提出了一种基于变分推理的贝叶斯卷积神经网络（BayesCNN）。此外，本文提出的BayesCNN结构也被应用于图像分类、图像超分辨率和生成性对抗网络等任务中。BayesCNN是基于Bayes的反向传播模型，由此推导出真实后验的变分近似。我们提出的方法不仅在相同的架构中达到等同于频率推断的性能，而且还包含不确定性和正则化的测量，还进一步消除了模型中使用的dropout技术。此外，我们预测了基于认知和任意不确定性模型预测的确定性，最后，我们提出了修剪贝叶斯结构的方法，使其更具计算性和时效性。本文第一部分介绍了贝叶斯神经网络，并将其应用到图像分类中，将相关结果与基于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，对结构进行了修剪，并对结果进行了比较。在论文的第二部分，这个概念被进一步应用到其他计算机视觉任务中，即图像超分辨率和生成对抗网络。对BayesCNN的概念进行了检验，并与同类领域中的其他概念进行了比较。

Artificial Neural Networks areconnectionist systems that perform a given task by learning on examples withouthaving prior knowledge about the task. This is done by finding an optimal pointestimate for the weights in every node. Generally, the network using point estimatesas weights perform well with large datasets, but they fail to expressuncertainty in regions with little or no data, leading to overconfidentdecisions.

In this thesis, Bayesian ConvolutionalNeural Network (BayesCNN) using Variational Inference is proposed, thatintroduces probability distribution over the weights. Furthermore, the proposedBayesCNN architecture is applied to tasks like Image Classification, ImageSuper-Resolution and Generative Adversarial Networks. BayesCNN is based onBayes by Backprop which derives a variational approximation to the trueposterior. Our proposed method not only achieves performances equivalent to frequentistinference in identical architectures but also incorporate a measurement for uncertaintiesand 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 aleatoricuncertainties and finally, we propose ways to prune the Bayesian architecture andto make it more computational and time effective. In the first part of thethesis, the Bayesian Neural Network is explained and it is applied to an ImageClassification task. The results are compared to point-estimates based architectureson MNIST, CIFAR-10, and CIFAR-100 datasets. Moreover, uncertainties are calculatedand the architecture is pruned and a comparison between the results is drawn. Inthe second part of the thesis, the concept is further applied to other computervision tasks namely, Image Super-Resolution and Generative AdversarialNetworks. The concept of BayesCNN is tested and compared against other conceptsin a similar domain.

1. 引言

2. 项目背景

3. 相关工作

4. 相关概念

5. 实验分析

6. 实际应用

7. 结论与未来展望

附录A 实验规范

附录B 如何复制结果

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