Definition: 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: We address the problem of general supervised learning when data can only be ac-<lb>cessed through an (indefinite) similarity function between data points. Existing<lb>work on learning with indefinite kernels has concentrated solely on binary/multi-<lb>class classification problems. We propose a model that is generic enough to handle<lb>any supervised learning task and also subsumes the model previously proposed for<lb>classification. We give a “goodness” criterion for similarity functions w.r.t. a given<lb>supervised learning task and then adapt a well-known landmarking technique to<lb>provide efficient algorithms for supervised learning using “good” similarity func-<lb>tions. We demonstrate the effectiveness of our model on three important super-<lb>vised learning problems: a) real-valued regression, b) ordinal regression and c)<lb>ranking where we show that our method guarantees bounded generalization error.<lb>Furthermore, for the case of real-valued regression, we give a natural goodness<lb>definition that, when used in conjunction with a recent result in sparse vector re-<lb>covery, guarantees a sparse predictor with bounded generalization error. Finally,<lb>we report results of our learning algorithms on regression and ordinal regression<lb>tasks using non-PSD similarity functions and demonstrate the effectiveness of<lb>our algorithms, especially that of the sparse landmark selection algorithm that<lb>achieves significantly higher accuracies than the baseline methods while offering<lb>reduced computational costs.

Supervised Learning with Similarity Functions