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.

[EX Q]: Collaborative data consist of ratings relating two distinct sets of objects: users and items. Much of the work with such data focuses on filtering: predicting unknown ratings for pairs of users and items. In this paper we focus on the problem of visualizing the information. Given all of the ratings, our task is to embed all of the users and items as points in the same Euclidean space. We would like to place users near items that they have rated (or would rate) high, and far away from those they would give low ratings. We pose this problem as a real-valued non-linear Bayesian network and employ Markov chain Monte Carlo and expectation maximization to find an embedding. We present a metric by which to judge the quality of a visualization and compare our results to Eigentaste, locally linear embedding and cooccurrence data embedding on three real-world datasets.
[EX A]: Visualization of Collaborative Data

[EX Q]: Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we propose a novel approach for classifying the rule languages with finite chase. Using this approach, a family of decidable rule languages, which extend the existing languages with the finite chase property, are naturally defined. We then study the complexity of these languages. Although all of them are tractable for data complexity, we show that their combined complexity can be arbitrarily high. Furthermore, we prove that all the rule languages with finite chase that extend the weakly acyclic language are of the same expressiveness as the weakly acyclic one, while rule languages with higher combined complexity are in general more succinct than those with lower combined complexity.
[EX A]: Existential Rule Languages with Finite Chase: Complexity and Expressiveness

[EX Q]: We propose a general method called truncated gradient to induce sparsity in the weights of online learning algorithms with convex loss functions. This method has several essential properties: 1. The degree of sparsity is continuous a parameter controls the rate of sparsi cation from no sparsi cation to total sparsi cation. 2. The approach is theoretically motivated, and an instance of it can be regarded as an online counterpart of the popular L1-regularization method in the batch setting. We prove that small rates of sparsi cation result in only small additional regret with respect to typical online learning guarantees. 3. The approach works well empirically. We apply the approach to several datasets and nd that for datasets with large numbers of features, substantial sparsity is discoverable.
[EX A]:
Sparse Online Learning via Truncated Gradient