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: Joint matching over a collection of objects aims at aggregating information from a large collection of similar instances (e.g. images, graphs, shapes) to improve maps between pairs of them. Given multiple objects and matches computed between a few object pairs in isolation, the goal is to recover an entire collection of maps that are (1) globally consistent, and (2) close to the provided maps — and under certain conditions provably the ground-truth maps. Despite recent advances on this problem, the best-known recovery guarantees are limited to a small constant barrier — none of the existing methods find theoretical support when more than 50% of input correspondences are corrupted. Moreover, prior approaches focus mostly on fully similar objects, while it is practically more demanding to match instances that are only partially similar to each other (e.g., different views of a single physical object). In this paper, we propose an algorithm to jointly match multiple objects that exhibit only partial similarities, given a few (possibly highly incomplete) pairwise matches that are densely corrupted. By encoding a consistent partial map collection into a 0-1 semidefinite matrix, we propose to recover the ground-truth maps via a parameter-free convex program called MatchLift, following a spectral method that pre-estimates the total number of distinct elements to be matched. Numerically, this program can be efficiently solved via alternating direction methods of multipliers (ADMM) along with a greedy rounding strategy. Theoretically, MatchLift exhibits near-optimal error-correction ability, i.e. in the asymptotic regime it is guaranteed to work even when a dominant fraction 1 − Θ ( log n √ n ) of the input maps behave like random outliers. Furthermore, MatchLift succeeds with minimal input complexity, namely, perfect matching can be achieved as soon as the provided maps form a connected map graph. We evaluate the proposed algorithm on various benchmark data sets including synthetic examples and real-world examples, all of which confirm the practical applicability and usefulness of MatchLift.
Example Output: Near-Optimal Joint Object Matching via Convex Relaxation

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: Connectionist Temporal Classification has recently attracted a lot of interest as it offers an elegant approach to building acoustic models (AMs) for speech recognition. The CTC loss function maps an input sequence of observable feature vectors to an output sequence of symbols. Output symbols are conditionally independent of each other under CTC loss, so a language model (LM) can be incorporated conveniently during decoding, retaining the traditional separation of acoustic and linguistic components in ASR. For fixed vocabularies, Weighted Finite State Transducers provide a strong baseline for efficient integration of CTC AMs with n-gram LMs. Character-based neural LMs provide a straight forward solution for open vocabulary speech recognition and all-neural models, and can be decoded with beam search. Finally, sequence-to-sequence models can be used to translate a sequence of individual sounds into a word string. We compare the performance of these three approaches, and analyze their error patterns, which provides insightful guidance for future research and development in this important area.
Example Output:
Comparison of Decoding Strategies for CTC Acoustic Models