Social Learning and Distributed Hypothesis Testing
Social Learning and Distributed Hypothesis Testing
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DOI：
10.1109/tit.2018.2837050
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发表时间：
2018-09-01
影响因子：
2.5
通讯作者：
Sarwate, Anand D.
中科院分区：
文献类型：
--
作者：
Lalitha, Anusha;Javidi, Tara;Sarwate, Anand D.
研究了网络环境下的分布式假设检验问题。网络中的各个节点接收噪声局部（私有）观测，其分布由离散参数（假设）参数化。以每个假设为条件的联合观测分布的边缘在节点处是局部已知的，但真实的参数/假设是未知的。一个更新规则进行分析，其中节点首先执行贝叶斯更新他们的信念（分布估计）的每个假设的基础上，他们的本地观测，这些更新他们的邻居，然后执行“非贝叶斯”的线性共识使用他们的邻居的对数信念。在温和的假设下，我们证明了任何节点的信念在一个错误的假设收敛到零指数快速。我们用节点对网络的影响和观测分布之间的分歧来描述学习的指数速率，我们称之为网络分歧。对于一类广泛的观测统计量，其中包括具有无界支持的分布，如高斯混合，我们证明了错误假设的拒绝率满足大偏差原则，即，假设拒绝率偏离平均率的样本路径的概率以指数形式快速消失，并根据节点对网络的影响和局部观测模型刻画了率函数。
This paper considers a problem of distributed hypothesis testing over a network. Individual nodes in a network receive noisy local (private) observations whose distribution is parameterized by a discrete parameter (hypothesis). The marginals of the joint observation distribution conditioned on each hypothesis are known locally at the nodes, but the true parameter/hypothesis is not known. An update rule is analyzed in which nodes first perform a Bayesian update of their belief (distribution estimate) of each hypothesis based on their local observations, communicate these updates to their neighbors, and then perform a "non-Bayesian" linear consensus using the log-beliefs of their neighbors. Under mild assumptions, we show that the belief of any node on a wrong hypothesis converges to zero exponentially fast. We characterize the exponential rate of learning, which we call the network divergence, in terms of the nodes' influence of the network and the divergences between the observations' distributions. For a broad class of observation statistics which includes distributions with unbounded support such as Gaussian mixtures, we show that rate of rejection of wrong hypothesis satisfies a large deviation principle, i.e., the probability of sample paths on which the rate of rejection of wrong hypothesis deviates from the mean rate vanishes exponentially fast and we characterize the rate function in terms of the nodes' influence of the network and the local observation models.