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State-of-the-art computer vision models are rapidly increasing in capacity, where the number of parameters far exceeds the number required to fit the training set. This results in better optimization and generalization performance. However, the huge size of contemporary models results in large inference costs and limits their use on resource-limited devices. In order to reduce inference costs, convolutional filters in trained neural networks could be pruned to reduce the run-time memory and computational requirements during inference. However, severe post-training pruning results in degraded performance if the training algorithm results in dense weight vectors. We propose the use of Batch Bridgeout, a sparsity inducing stochastic regularization scheme, to train neural networks so that they could be pruned efficiently with minimal degradation in performance. We evaluate the proposed method on common computer vision models VGGNet, ResNet, and Wide-ResNet on the CIFAR image classification task. For all the networks, experimental results show that Batch Bridgeout trained networks achieve higher accuracy across a wide range of pruning intensities compared to Dropout and weight decay regularization.