Section: New Results

Decentralized Estimation in Networks

In [3] , we studied the problem of decentralized estimation in networks, where each node of the network holds a data point and the goal is to estimate some statistics on the entire data under communication constraints imposed by the graph topology of the network. This generic problem has many applications in Internet of Things as well as for extracting knowledge from massive information graphs such as interlinked Web documents and online social media. In this work, we focused on estimating pairwise mean statistics. Popular examples of such statistics include the sample variance, the average distance and the Area Under the ROC Curve, among others. We proposed new synchronous and asynchronous randomized gossip algorithms which simultaneously propagate data across the network and maintain local estimates of the quantity of interest. We establish convergence rate bounds of $O(1/t)$ and $O(logt/t)$ for the synchronous and asynchronous cases respectively, where $t$ is the number of iterations, with explicit data and network dependent terms. Beyond favorable comparisons in terms of rate analysis, numerical experiments provide empirical evidence the proposed algorithms surpasses the previously introduced approach.