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.
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Question: In many applications spanning from sensor to social networks, transportation systems, gene regulatory networks or big data, the signals of interest are defined over the vertices of a graph. The aim of this paper is to propose a least mean square (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment.

Answer: Least Mean Squares Estimation of Graph Signals


Question: Despite the increasing use of social media platforms for information and news gathering, its unmoderated nature often leads to the emergence and spread of rumours, i.e. pieces of information that are unverified at the time of posting. At the same time, the openness of social media platforms provides opportunities to study how users share and discuss rumours, and to explore how natural language processing and data mining techniques may be used to find ways of determining their veracity. In this survey we introduce and discuss two types of rumours that circulate on social media; long-standing rumours that circulate for long periods of time, and newly-emerging rumours spawned during fast-paced events such as breaking news, where reports are released piecemeal and often with an unverified status in their early stages. We provide an overview of research into social media rumours with the ultimate goal of developing a rumour classification system that consists of four components: rumour detection, rumour tracking, rumour stance classification and rumour veracity classification. We delve into the approaches presented in the scientific literature for the development of each of these four components. We summarise the efforts and achievements so far towards the development of rumour classification systems and conclude with suggestions for avenues for future research in social media mining for detection and resolution of rumours.

Answer: Detection and Resolution of Rumours in Social Media: A Survey


Question: Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for general-sum stochastic games by Filar and Vrieze [2004]. However, the optimization problem there has a non-linear objective and non-linear constraints with special structure. Since gradients of both the objective as well as constraints of this optimization problem are well defined, gradient based schemes seem to be a natural choice. We discuss a gradient scheme tuned for two-player stochastic games. We show in simulations that this scheme indeed converges to a Nash equilibrium, for a simple terrain exploration problem modelled as a general-sum stochastic game. However, it turns out that only global minima of the optimization problem correspond to Nash equilibria of the underlying general-sum stochastic game, while gradient schemes only guarantee convergence to local minima. We then provide important necessary conditions for gradient schemes to converge to Nash equilibria in general-sum stochastic games.

Answer:
A Study of Gradient Descent Schemes for General-Sum Stochastic Games