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 paper, 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. The results are compared to point-estimates based architectures on MNIST, CIFAR-10 and CIFAR-100 datasets for Image CLassification task, on BSD300 dataset for Image Super Resolution task and on CIFAR10 dataset again for Generative Adversarial Network task. BayesCNN is based on Bayes by Backprop which derives a variational approximation to the true posterior. We, therefore, introduce the idea of applying two convolutional operations, one for the mean and one for the variance. 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 empirically show how the uncertainty can decrease, allowing the decisions made by the network to become more deterministic as the training accuracy increases. Finally, we propose ways to prune the Bayesian architecture and to make it more computational and time effective.

* arXiv admin note: text overlap with arXiv:1506.02158, arXiv:1703.04977 by other authors
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We introduce Bayesian Convolutional Neural Networks (BayesCNNs), a variant of Convolutional Neural Networks (CNNs) which is built upon Bayes by Backprop. We demonstrate how this novel reliable variational inference method can serve as a fundamental construct for various network architectures. On multiple datasets in supervised learning settings (MNIST, CIFAR-10, CIFAR-100, and STL-10), our proposed variational inference method achieves performances equivalent to frequentist inference in identical architectures, while a measurement for uncertainties and a regularisation are incorporated naturally. In the past, Bayes by Backprop has been successfully implemented in feedforward and recurrent neural networks, but not in convolutional ones. This work symbolises the extension of Bayesian neural networks which encompasses all three aforementioned types of network architectures now.

* arXiv admin note: text overlap with arXiv:1704.02798 by other authors
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