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.
Tangent Prop @cite_20 is a way to avoid over-fitting with implicit use of data augmentation. Virtual samples are used to compute the regularization term that is defined as the sum of tangent distances, each of which is the distance between an original sample and a slightly deformed one. It is expected that classifier's output is stable in the vicinity of original data points, but not necessarily so in other locations.
@cite_20
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In pattern recognition, statistical modeling, or regression, the amount of data is a critical factor affecting the performance. If the amount of data and computational resources are unlimited, even trivial algorithms will converge to the optimal solution. However, in the practical case, given limited data and other resources, satisfactory performance requires sophisticated methods to regularize the problem by introducing a priori knowledge. Invariance of the output with respect to certain transformations of the input is a typical example of such a priori knowledge. In this chapter, we introduce the concept of tangent vectors, which compactly represent the essence of these transformation invariances, and two classes of algorithms, “tangent distance” and “tangent propagation”, which make use of these invariances to improve performance. The ever-increasing size of modern datasets combined with the difficulty of obtaining label information has made semi-supervised learning of significant practical importance in modern machine learning applications. Compared with supervised learning, the key difficulty in semi-supervised learning is how to make full use of the unlabeled data. In order to utilize manifold information provided by unlabeled data, we propose a novel regularization called the tangent-normal adversarial regularization, which is composed by two parts. The two terms complement with each other and jointly enforce the smoothness along two different directions that are crucial for semi-supervised learning. One is applied along the tangent space of the data manifold, aiming to enforce local invariance of the classifier on the manifold, while the other is performed on the normal space orthogonal to the tangent space, intending to impose robustness on the classifier against the noise causing the observed data deviating from the underlying data manifold. Both of the two regularizers are achieved by the strategy of virtual adversarial training. Our method has achieved state-of-the-art performance on semi-supervised learning tasks on both artificial dataset and FashionMNIST dataset. NLP models have many and sparse features, and regularization is key for balancing model overfitting versus underfitting. A recently repopularized form of regularization is to generate fake training data by repeatedly adding noise to real data. We reinterpret this noising as an explicit regularizer, and approximate it with a second-order formula that can be used during training without actually generating fake data. We show how to apply this method to structured prediction using multinomial logistic regression and linear-chain CRFs. We tackle the key challenge of developing a dynamic program to compute the gradient of the regularizer efficiently. The regularizer is a sum over inputs, so we can estimate it more accurately via a semi-supervised or transductive extension. Applied to text classification and NER, our method provides a >1 absolute performance gain over use of standardL2 regularization. Distance measure is quite important for pattern recognition. Utilizing invariance in image data, tangent distance is very powerful in classifying handwritten digits. For this measure a set of invariant transformations must be known a priori. But in many practical problems, it is very difficult to know these transformations. In this paper, an algorithm is proposed to approximate the invariant tangent distance exclusively from the data. By virtue of ideas arising from manifold learning, the algorithm needs no prior transformations and can be applied to more classification problems. k-nearest neighbor rule based on the new distance are implemented for classification problems. Experimental results on synthetic and real datasets illustrate its validity.