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: In this paper, we propose the distributed tree kernels (DTK) as a novel method to reduce time and space complexity of tree kernels. Using a linear complexity algorithm to compute vectors for trees, we embed feature spaces of tree fragments in low-dimensional spaces where the kernel computation is directly done with dot product. We show that DTKs are faster, correlate with tree kernels, and obtain a statistically similar performance in two natural language processing tasks.

Output: Distributed Tree Kernels


Input: Consider Input: Various tasks in decision making and decision support systems require selecting a preferred subset of a given set of items. Here we focus on problems where the individual items are described using a set of characterizing attributes, and a generic preference specification is required, that is, a specification that can work with an arbitrary set of items. For example, preferences over the content of an online newspaper should have this form: At each viewing, the newspaper contains a subset of the set of articles currently available. Our preference specification over this subset should be provided offline, but we should be able to use it to select a subset of any currently available set of articles, e.g., based on their tags. We present a general approach for lifting formalisms for specifying preferences over objects with multiple attributes into ones that specify preferences over subsets of such objects. We also show how we can compute an optimal subset given such a specification in a relatively efficient manner. We provide an empirical evaluation of the approach as well as some worst-case complexity results.

Output: Generic Preferences over Subsets of Structured Objects


Input: Consider Input: Nearest neighbor methods are a popular class of nonparametric estimators with several<lb>desirable properties, such as adaptivity to different distance scales in different regions of<lb>space. Prior work on convergence rates for nearest neighbor classification has not fully<lb>reflected these subtle properties. We analyze the behavior of these estimators in metric<lb>spaces and provide finite-sample, distribution-dependent rates of convergence under min-<lb>imal assumptions. As a by-product, we are able to establish the universal consistency of<lb>nearest neighbor in a broader range of data spaces than was previously known. We illus-<lb>trate our upper and lower bounds by introducing smoothness classes that are customized<lb>for nearest neighbor classification.


Output: Rates of Convergence for Nearest Neighbor Classification