Autoencoders are widely used for unsupervised learning and as a regularization scheme in semi-supervised learning. However, theoretical understanding of their generalization properties and of the manner in which they can assist supervised learning has been lacking. We utilize recent advances in the theory of deep learning generalization, together with a novel reconstruction loss, to provide generalization bounds for autoencoders. To the best of our knowledge, this is the first such bound. We further show that, under appropriate assumptions, an autoencoder with good generalization properties can improve any semi-supervised learning scheme. We support our theoretical results with empirical demonstrations.
@cite_10 provide a principled approach to feature representation, and characterize the relation between the information retained by features about the input, and the loss incurred by a classifier based on these features. They suggest the application of their results to SSL, but do not provide explicit conditions or generalization bounds in this setting. Recently, @cite_26 provide such bounds for semi-supervised learning with linear AEs and a joint reconstruction classification loss, using uniform stability arguments. They also provide empirical results that show that nonlinear AEs can indeed contribute to supervised learning. While their results are close in spirit to ours, we are more concerned with understanding how the structure of the data affects SSL, and, in particular, characterizing when, and to what extent, clustering of the input contributes to performance through unsupervised learning. Moreover, we rely on bounds that are specific to neural networks, rather than on the looser stability based bounds.
@cite_26 @cite_10
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Empirical evidence shows that in favorable situations semi-supervised learning (SSL) algorithms can capitalize on the abundance of unlabeled training data to improve the performance of a learning task, in the sense that fewer labeled training data are needed to achieve a target error bound. However, in other situations unlabeled data do not seem to help. Recent attempts at theoretically characterizing SSL gains only provide a partial and sometimes apparently conflicting explanations of whether, and to what extent, unlabeled data can help. In this paper, we attempt to bridge the gap between the practice and theory of semi-supervised learning. We develop a finite sample analysis that characterizes the value of un-labeled data and quantifies the performance improvement of SSL compared to supervised learning. We show that there are large classes of problems for which SSL can significantly outperform supervised learning, in finite sample regimes and sometimes also in terms of error convergence rates. The problem of learning a mapping between input and structured, interdependent output variables covers sequential, spatial, and relational learning as well as predicting recursive structures. Joint feature representations of the input and output variables have paved the way to leveraging discriminative learners such as SVMs to this class of problems. We address the problem of semi-supervised learning in joint input output spaces. The co-training approach is based on the principle of maximizing the consensus among multiple independent hypotheses; we develop this principle into a semi-supervised support vector learning algorithm for joint input output spaces and arbitrary loss functions. Experiments investigate the benefit of semi-supervised structured models in terms of accuracy and F1 score. The insufficiency of labeled training data is a major obstacle in automatic image annotation. To tackle this problem, we propose a semi-supervised manifold kernel density estimation (SSMKDE) approach based on a recently proposed manifold KDE method. Our contributions are twofold. First, SSMKDE leverages both labeled and unlabeled samples and formulates all data in a manifold structure, which enables a more accurate label prediction. Second, the relationship between KDE-based methods and graph-based semi-supervised learning (SSL) methods is analyzed, which helps to better understand graph-based SSL methods. Extensive experiments demonstrate the superiority of SSMKDE over existing KDE-based and graph-based SSL methods. This paper presents a novel feature learning model for cyber security tasks. We propose to use Auto-encoders (AEs), as a generative model, to learn latent representation of different feature sets. We show how well the AE is capable of automatically learning a reasonable notion of semantic similarity among input features. Specifically, the AE accepts a feature vector, obtained from cyber security phenomena, and extracts a code vector that captures the semantic similarity between the feature vectors. This similarity is embedded in an abstract latent representation. Because the AE is trained in an unsupervised fashion, the main part of this success comes from appropriate original feature set that is used in this paper. It can also provide more discriminative features in contrast to other feature engineering approaches. Furthermore, the scheme can reduce the dimensionality of the features thereby signicantly minimising the memory requirements. We selected two different cyber security tasks: networkbased anomaly intrusion detection and Malware classication. We have analysed the proposed scheme with various classifiers using publicly available datasets for network anomaly intrusion detection and malware classifications. Several appropriate evaluation metrics show improvement compared to prior results.