Large Deviations Performance of Consensus+Innovations Distributed Detection with Non-Gaussian Observations

Abstract

We establish the large deviations asymptotic performance (error exponent) of consensus+innovations distributed detection over random networks with generic (non-Gaussian) sensor observations. At each time instant, sensors 1) combine theirs with the decision variables of their neighbors (consensus) and 2) assimilate their new observations (innovations). This paper shows for general non-Gaussian distributions that consensus+innovations distributed detection exhibits a phase transition behavior with respect to the network degree of connectivity. Above a threshold, distributed is as good as centralized, with the same optimal asymptotic detection performance, but, below the threshold, distributed detection is suboptimal with respect to centralized detection. We determine this threshold and quantify the performance loss below threshold. Finally, we show the dependence of the threshold and performance on the distribution of the observations: distributed detectors over the same random network, but with different observations' distributions, for example, Gaussian, Laplace, or quantized, may have different asymptotic performance, even when the corresponding centralized detectors have the same asymptotic performance.

30 pages, journal, submitted Nov 17, 2011; revised Apr 3, 2012

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• Sensor Selection for Event Detection in Wireless Sensor Networks
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• Diffusion-Based Adaptive Distributed Detection: Steady-State Performance in the Slow Adaptation Regime
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• Networked Signal and Information Processing
• Local Tomography of Large Networks under the Low-Observability Regime
• FADE: Fast and Asymptotically efficient Distributed Estimator for dynamic networks
• Distributed inference over directed networks: Performance limits and optimal design
• Causal Influence in Federated Edge Inference
• Distributed Detection in Ad Hoc Networks Through Quantized Consensus