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.

Example Input: This paper deals with the problem of esti mating the probability that one event was a cause of another in a given scenario. Us ing structural-semantical definitions of the probabilities of necessary or sufficient cau sation (or both), we show how to optimally bound these quantities from data obtained in experimental and observational studies, making minimal assumptions concerning the data-generating process. In particular, we strengthen the results of Pearl (1999) by weakening the data-generation assumptions and deriving theoretically sharp bounds on the probabilities of causation. These results delineate precisely how empirical data can be used both in settling questions of attribution and in solving attribution-related problems of decision making.
Example Output: Probabilities of Causation: Bounds and Identification

Example 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.
Example Output: Dropout Training as Adaptive Regularization

Example Input: As a well-known NP-hard problem, the Three-Index Assignment Problem (AP3) has attracted lots of research efforts for developing heuristics. However, existing heuristics either obtain less competitive solutions or consume too much running time. In this paper, a new heuristic named Approximate Muscle guided Beam Search (AMBS) is developed to achieve a good trade-off between solution quality and running time. By combining the approximate muscle with beam search, the solution space size can be significantly decreased, thus the time for searching the solution can be sharply reduced. Extensive experimental results on the benchmark indicate that the new algorithm is able to obtain solutions with competitive quality and it can be employed on instances with large-scale. Work of this paper not only proposes a new efficient heuristic, but also provides a promising method to improve the efficiency of beam search.
Example Output:
Approximate Muscle Guided Beam Search for Three-Index Assignment Problem