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.

Q: Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.

A: Top-N Recommendation on Graphs
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Q: We propose a novel approach to automatically produce multiple colorized versions of a grayscale image. Our method results from the observation that the task of automated colorization is relatively easy given a low-resolution version of the color image. We first train a conditional PixelCNN to generate a low resolution color for a given grayscale image. Then, given the generated low-resolution color image and the original grayscale image as inputs, we train a second CNN to generate a high-resolution colorization of an image. We demonstrate that our approach produces more diverse and plausible colorizations than existing methods, as judged by human raters in a ”Visual Turing Test”.

A: PIXCOLOR: PIXEL RECURSIVE COLORIZATION
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Q: The AGM theory of belief revision has be­ come an important paradigm for investigat­ ing rational belief changes. Unfortunately, researchers working in this paradigm have re­ stricted much of their attention to rather sim­ ple representations of belief states, namely logically closed sets of propositional sen­ tences. In our opinion, this has resulted in a too abstract categorisation of belief change operations: expansion, revision, or contrac­ tion. Occasionally, in the AGM paradigm, also probabilistic belief changes have been considered, and it is widely accepted that the probabilistic version of expansion is con­ ditioning. However, we argue that it may be more correct to view conditioning and expan­ sion as two essentially different kinds of belief change, and that what we call constraining is a better candidate for being considered prob­ abilistic expansion.

A:
Probabilistic Belief Change: Expansion, Conditioning and Constraining
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