Distributed SPS algorithms for non-asymptotic confidence region evaluation

Abstract

In this paper, the distributed computation of confidence regions for parameter estimation is considered. Some information diffusion strategies are proposed and compared in terms of the required number of data exchanges to get the corresponding region. The effects of algorithms truncation is also addressed. As support for the theoretical part, numerical results are presented.

Distributed Nonasymptotic Confidence Region Computation Over Sensor Networks

“…It is compared with classical general purpose information diffusion strategies, such as flooding [2], [25] and consensus algorithms [11], in terms of generated traffic load as well as of confidence region volume/traffic trade-off. Performance predictions, simulation and experimental results are provided for various topologies, extending preliminary results presented in [1].…”

“…In [1] we showed that confidence regions, as defined by SPS, may be evaluated in a distributed way, for example in wireless sensor networks (WSNs). For that purpose, the nodes share their local information with each other and the confidence region computation is performed locally.…”

“…For that purpose, the nodes share their local information with each other and the confidence region computation is performed locally. Three information diffusion approaches (data flooding and parallel in-node processing, distributed processing via average consensus, and mixed flooding+consensus) have been considered in [1] to provide each node with the information allowing a distributed computation of the confidence region.…”

“…, n are assumed to be statistically independent and to follow a symmetrical distribution. 1 Deterministic regressors ϕ i are considered here, but this work may be extended to the case of random exogenous regressors, i.e., regressors ϕ i s that are independent on the noise terms. We consider the worst case in which the value of ϕ i is assumed known only by Node i.…”

“…It defines an exact confidence region around the least 1 In [23], no symmetry condition is considered, the random measurement sequence is only assumed to form an exchangeable sequence of random variables. This work readily extends to this alternative assumption.…”