Consensus and Approximation-based Distribution Statistics in Network Systems
Yushan Li, Qing Jiao, Han Wang, Jianping He · 2021
The data distribution statistics in network systems have gained increasing attention. In this paper, we study the problem of obtaining the global probability density function (PDF) across the network, where each agent only holds a portion of the overall distribution in the network. Our work significantly deviates from traditional distribution/density problems, which infer the underlying common distribution from multiple i.i.d. random samples. The agents initially hold interval-wise and related data distribution, and no central node is required while no prior knowledge about the network structure is available. To practice, we propose a novel consensus and approximation-based distribution statistics (CADS) algorithm. The key insight is utilizing polynomials to approximate the initial distribution function of each agent, such that a unified and compact representation for various function forms is used to improve the storage flexibility and computation efficiency during the consensus-based interaction rounds. Another salient design is that when the intervals of all agents are different, the proposed algorithm is able to adapt the dynamically changing interval range, and avoid massive interval storage cost by a refit operation for large-scale networks. We prove the convergence and the bounded PDF approximation error of the proposed algorithm, and analyze the statistics performance and algorithm complexity. Simulations illustrate the effectiveness of the CADS algorithm.