TASK 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.
PROBLEM: This manuscript presents a trust computation for international relations and its calculus, which related to Bayesian inference, Dempster-Shafer theory and subjective logic. We proposed a method that allows a trust computation which is previously subjective and incomputable. An example of case study for the trust computation is the United States of America–Great Britain relations. The method supports decision makers in a government such as foreign ministry, defense ministry, presidential or prime minister office. The Department of Defense (DoD) may use our method to determine a nation that can be known as a friendly, neutral or hostile nation.

SOLUTION: A Mathematical Trust Algebra for International Nation Relations Computation and Evaluation

PROBLEM: The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems.

SOLUTION: Flexible Multi-layer Sparse Approximations of Matrices and Applications

PROBLEM: Recursive neural models, which use syntactic parse trees to recursively generate representations bottom-up from parse children, are a popular new architecture, promising to capture structural properties like the scope of negation or long-distance semantic dependencies. But understanding exactly which tasks this parse-based method is appropriate for remains an open question. In this paper we benchmark recursive neural models against sequential recurrent neural models, which are structured solely on word sequences. We investigate 5 tasks: sentiment classification on (1) sentences and (2) syntactic phrases; (3) question answering; (4) discourse parsing; (5) semantic relations (e.g., component-whole between nouns); We find that recurrent models have equal or superior performance to recursive models on all tasks except one: semantic relations between nominals. Our analysis suggests that tasks relying on the scope of negation (like sentiment) are well-handled by sequential models. Recursive models help only with tasks that require representing long-distance relations between words. Our results offer insights on the design of neural architectures for representation learning.

SOLUTION:
When Are Tree Structures Necessary for Deep Learning of Representations?