Efficient Bayesian Learning in Social Networks with Gaussian Estimators
Efficient Bayesian Learning in Social Networks with Gaussian Estimators
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使用高斯估计器在社交网络中进行高效贝叶斯学习
DOI：
10.1109/allerton.2016.7852262
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
O. Tamuz
中科院分区：
文献类型：
--
作者：
Elchanan Mossel;Noah Olsman;O. Tamuz
我们考虑一组贝叶斯代理，他们试图通过社交网络上的交互来估计世界的状态θ。每个智能体v最初都会收到一个私人的θ测量值：一个从具有平均值θ和标准差σ的高斯分布中选取的数字Sv。然后，在每个离散时间迭代中，每个都向其邻居揭示其θ的估计，并观察其邻居的行为，使用贝叶斯定律更新其信念。这个过程有效地聚集了信息，在这个意义上，所有的代理人都收敛到他们会有的信念，如果他们能够访问所有的私人测量。我们表明，这个过程是计算效率，使每个代理的计算可以很容易地进行。我们还证明了在任何图上，该过程在至多2N · D步后收敛，其中N是代理的数量，D是网络的直径。最后，我们表明，在树上和距离传递图的过程收敛后D步骤，它保留隐私，使代理人很少了解大多数其他代理人的私人信号，尽管有效的信息聚合。我们的研究结果扩展了第一和最后一位作者未发表的手稿。
We consider a group of Bayesian agents who try to estimate a state of the world θ through interaction on a social network. Each agent v initially receives a private measurement of θ: a number Sv picked from a Gaussian distribution with mean θ and standard deviation σ. Then, in each discrete time iteration, each reveals its estimate of θ to its neighbors, and, observing its neighbors' actions, updates its belief using Bayes' Law. This process aggregates information efficiently, in the sense that all the agents converge to the belief that they would have, had they access to all the private measurements. We show that this process is computationally efficient, so that each agent's calculation can be easily carried out. We also show that on any graph the process converges after at most 2N · D steps, where N is the number of agents and D is the diameter of the network. Finally, we show that on trees and on distance-transitive graphs the process converges after D steps, and that it preserves privacy, so that agents learn very little about the private signal of most other agents, despite the efficient aggregation of information. Our results extend those in an unpublished manuscript of the first and last authors.