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: Determinantal Point Processes (Dpps) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks such as sampling. In light of this, we propose a new method for approximate sampling from discrete k-Dpps. Our method takes advantage of the diversity property of subsets sampled from a Dpp, and proceeds in two stages: first it constructs coresets for the ground set of items; thereafter, it efficiently samples subsets based on the constructed coresets. As opposed to previous approaches, our algorithm aims to minimize the total variation distance to the original distribution. Experiments on both synthetic and real datasets indicate that our sampling algorithm works efficiently on large data sets, and yields more accurate samples than previous approaches.

A: Efficient Sampling for k-Determinantal Point Processes
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Q: The folksonomy is the result of free personal information or assignment of tags to an object (determined by the URI) in order to find them. The practice of tagging is done in a collective environment. Folksonomies are self constructed, based on co-occurrence of definitions, rather than a hierarchical structure of the data. The downside of this was that a few sites and applications are able to successfully exploit the sharing of bookmarks. The need for tools that are able to resolve the ambiguity of the definitions is becoming urgent as the need of simple instruments for their visualization, editing and exploitation in web applications still hinders their diffusion and wide adoption. An intelligent interactive interface design for folksonomies should consider the contextual design and inquiry based on a concurrent interaction for a perceptual user interfaces. To represent folksonomies a new concept structure called "Folksodriven" is used in this paper. While it is presented the Folksodriven Structure Network (FSN) to resolve the ambiguity of definitions of folksonomy tags suggestions for the user. On this base a Human-Computer Interactive (HCI) systems is developed for the visualization, navigation, updating and maintenance of folksonomies Knowledge Bases the FSN through the web. System functionalities as well as its internal architecture will be introduced.

A: Intelligent Interface Architectures for Folksonomy Driven Structure Network
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Q: We study the problem of recovering an incomplete m n matrix of rank r with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer vision, system identification, etc. The challenge is to design provable algorithms tolerant to a large amount of noises, with small sample complexity. In this work, we give algorithms achieving strong guarantee under two realistic noise models. In bounded deterministic noise, an adversary can add any bounded yet unstructured noise to each column. For this problem, we present an algorithm that returns a matrix of a small error, with sample complexity almost as small as the best prior results in the noiseless case. For sparse random noise, where the corrupted columns are sparse and drawn randomly, we give an algorithm that exactly recovers an 0-incoherent matrix by probability at least 1 with sample complexity as small asO (0rn log(r/)). This result advances the state-of-the-art work and matches the lower bound in a worst case. We also study the scenario where the hidden matrix lies on a mixture of subspaces and show that the sample complexity can be even smaller. Our proposed algorithms perform well experimentally in both synthetic and real-world datasets.

A:
Noise-Tolerant Life-Long Matrix Completion via Adaptive Sampling
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