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 Input:
This manuscript presents a trust computation for international relations and its calculus, which related to Bayesian inference, Dempster-Shafer theory and subjective logic. We proposed a method that allows a trust computation which is previously subjective and incomputable. An example of case study for the trust computation is the United States of America–Great Britain relations. The method supports decision makers in a government such as foreign ministry, defense ministry, presidential or prime minister office. The Department of Defense (DoD) may use our method to determine a nation that can be known as a friendly, neutral or hostile nation.

Ex Output:
A Mathematical Trust Algebra for International Nation Relations Computation and Evaluation


Ex Input:
Quantifying the degree of spatial dependence for linguistic variables is a key task for analyzing dialectal variation. However, existing approaches have important drawbacks. First, they make unjustified assumptions about the nature of spatial variation: some assume that the geographical distribution of linguistic variables is Gaussian, while others assume that linguistic variation is aligned to pre-defined geopolitical units such as states or counties. Second, they are not applicable to all types of linguistic data: some approaches apply only to frequencies, others to boolean indicators of whether a linguistic variable is present. We present a new method for measuring geographical language variation, which solves both of these problems. Our approach builds on reproducing kernel Hilbert space (RKHS) representations for nonparametric statistics, and takes the form of a test statistic that is computed from pairs of individual geotagged observations without aggregation into predefined geographical bins. We compare this test with prior work using synthetic data as well as a diverse set of real datasets: a corpus of Dutch tweets, a Dutch syntactic atlas, and a dataset of letters to the editor in North American newspapers. Our proposed test is shown to support robust inferences across a broad range of scenarios and types of data.

Ex Output:
A Kernel Independence Test for Geographical Language Variation


Ex Input:
Dropout and other feature noising schemes control overfitting by artificially cor-<lb>rupting the training data. For generalized linear models, dropout performs a form<lb>of adaptive regularization. Using this viewpoint, we show that the dropout regular-<lb>izer is first-order equivalent to an L2 regularizer applied after scaling the features<lb>by an estimate of the inverse diagonal Fisher information matrix. We also establish<lb>a connection to AdaGrad, an online learning algorithm, and find that a close rel-<lb>ative of AdaGrad operates by repeatedly solving linear dropout-regularized prob-<lb>lems. By casting dropout as regularization, we develop a natural semi-supervised<lb>algorithm that uses unlabeled data to create a better adaptive regularizer. We ap-<lb>ply this idea to document classification tasks, and show that it consistently boosts<lb>the performance of dropout training, improving on state-of-the-art results on the<lb>IMDB reviews dataset.

Ex Output:

Dropout Training as Adaptive Regularization