Deep neural networks have been exhibiting splendid accuracies in many of visual pattern classification problems. Many of the state-of-the-art methods employ a technique known as data augmentation at the training stage. This paper addresses an issue of decision rule for classifiers trained with augmented data. Our method is named as APAC: the Augmented PAttern Classification, which is a way of classification using the optimal decision rule for augmented data learning. Discussion of methods of data augmentation is not our primary focus. We show clear evidences that APAC gives far better generalization performance than the traditional way of class prediction in several experiments. Our convolutional neural network model with APAC achieved a state-of-the-art accuracy on the MNIST dataset among non-ensemble classifiers. Even our multilayer perceptron model beats some of the convolutional models with recently invented stochastic regularization techniques on the CIFAR-10 dataset.
We present a probabilistic variant of the recently introduced maxout unit. The success of deep neural networks utilizing maxout can partly be attributed to favorable performance under dropout, when compared to rectified linear units. It however also depends on the fact that each maxout unit performs a pooling operation over a group of linear transformations and is thus partially invariant to changes in its input. Starting from this observation we ask the question: Can the desirable properties of maxout units be preserved while improving their invariance properties ? We argue that our probabilistic maxout (probout) units successfully achieve this balance. We quantitatively verify this claim and report classification performance matching or exceeding the current state of the art on three challenging image classification benchmarks (CIFAR-10, CIFAR-100 and SVHN).