The “component debiasing” method in distributed Byzantine problems

In the era of big data, there are three major problems of centralized estimation methods: inability to exist, inability to calculate and privacy protection, and distributed statistical methods have emerged based on them. Distributed computing involves the communication between multiple machines, and the existing statistical inference methods are difficult to apply due to the loss of estimator accuracy due to the accumulation of bias. Therefore, based on the method of "introducing component debiasing", this paper constructs a general parameter distributed estimation framework to solve the problem of distributed computing. Firstly, the real parameters are expressed as a function of multiple component parameters and the U statistic is introduced, and then the distributed estimation of the component parameters is carried out, and the median value is taken as the global estimator of the component parameters, and finally the final estimator of the real parameters is summarized. In this paper, a distributed BUDE algorithm is established, which performs the median aggregate local estimator to obtain the global estimator. The probability convergence boundary and asymptotic normality of the estimator are theoretically proved, and the simulation results show that the algorithm has more advantages than other methods, which illustrates the effectiveness of the proposed algorithm.