  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.
