In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies. Inference is shown to be PEXP-complete, and variational methods are designed so as to exploit logical inference whenever possible.
Complexity Analysis and Variational Inference for Interpretation-based Probabilistic Description Logics

The study of social networks is a burgeoning research area. However, most existing work deals with networks that simply encode whether relationships exist or not. In contrast, relationships in signed networks can be positive (“like”, “trust”) or negative (“dislike”, “distrust”). The theory of social balance shows that signed networks tend to conform to some local patterns that, in turn, induce certain global characteristics. In this paper, we exploit both local as well as global aspects of social balance theory for two fundamental problems in the analysis of signed networks: sign prediction and clustering. Motivated by local patterns of social balance, we first propose two families of sign prediction methods: measures of social imbalance (MOIs), and supervised learning using high order cycles (HOCs). These methods predict signs of edges based on triangles and l-cycles for relatively small values of l. Interestingly, by examining measures of social imbalance, we show that the classic Katz measure, which is used widely in unsigned link prediction, actually has a balance theoretic interpretation when applied to signed networks. Furthermore, motivated by the global structure of balanced networks, we propose an effective low rank modeling approach for both sign prediction and clustering. For the low rank modeling approach, we provide theoretical performance guarantees via convex relaxations, scale it up to large problem sizes using a matrix factorization based algorithm, and provide extensive experimental validation including comparisons with local approaches. Our experimental results indicate that, by adopting a more global viewpoint of balance structure, we get significant performance and computational gains in prediction and clustering tasks on signed networks. Our work therefore highlights the usefulness of the global aspect of balance theory for the analysis of signed networks.
Prediction and Clustering in Signed Networks: A Local to Global Perspective

Recently, recurrent neural networks (RNNs) as powerful sequence models have re-emerged as a potential acoustic model for statistical parametric speech synthesis (SPSS). The long short-term memory (LSTM) architecture is particularly attractive because it addresses the vanishing gradient problem in standard RNNs, making them easier to train. Although recent studies have demonstrated that LSTMs can achieve significantly better performance on SPSS than deep feedforward neural networks, little is known about why. Here we attempt to answer two questions: a) why do LSTMs work well as a sequence model for SPSS; b) which component (e.g., input gate, output gate, forget gate) is most important. We present a visual analysis alongside a series of experiments, resulting in a proposal for a simplified architecture. The simplified architecture has significantly fewer parameters than an LSTM, thus reducing generation complexity considerably without degrading quality.

INVESTIGATING GATED RECURRENT NETWORKS FOR SPEECH SYNTHESIS