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.

Input: Consider 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.

Output: A Kernel Independence Test for Geographical Language Variation


Input: Consider Input: The success of semi-supervised learning crucially relies on the scalability to a huge amount of unlabelled data that are needed to capture the underlying manifold structure for better classification. Since computing the pairwise similarity between the training data is prohibitively expensive in most kinds of input data, currently, there is no general readyto-use semi-supervised learning method/tool available for learning with tens of millions or more data points. In this paper, we adopted the idea of two low-rank label propagation algorithms, GLNP (Global Linear Neighborhood Propagation) and Kernel Nyström Approximation, and implemented the parallelized version of the two algorithms accelerated with Nesterov’s accelerated projected gradient descent for Big-data Label Propagation (BigLP). The parallel algorithms are tested on five real datasets ranging from 7000 to 10,000,000 in size and a simulation dataset of 100,000,000 samples. In the experiments, the implementation can scale up to datasets with 100,000,000 samples and hundreds of features and the algorithms also significantly improved the prediction accuracy when only a very small percentage of the data is labeled. The results demonstrate that the BigLP implementation is highly scalable to big data and effective in utilizing the unlabeled data for semi-supervised learning.

Output: Low-rank Label Propagation for Semi-supervised Learning with 100 Millions Samples


Input: Consider Input: Recommender systems often use latent features to explain the behaviors of users and capture the properties of items. As users interact with different items over time, user and item features can influence each other, evolve and co-evolve over time. To accurately capture the fine grained nonlinear coevolution of these features, we propose a recurrent coevolutionary feature embedding process model, which combines recurrent neural network (RNN) with a multidimensional point process model. The RNN learns a nonlinear representation of user and item features which take into account mutual influence between user and item features, and the feature evolution over time. We also develop an efficient stochastic gradient algorithm for learning the model parameters, which can readily scale up to millions of events. Experiments on diverse real-world datasets demonstrate significant improvements in user behavior prediction compared to state-of-the-arts.


Output: Recurrent Coevolutionary Feature Embedding Processes for Recommendation