Efficient linear fusion of partial estimators

Many signal processing applications require performing statistical inference on large datasets, where computational and/or memory restrictions become an issue. In this big data setting, computing an exact global centralized estimator is often either unfeasible or impractical. Hence, several authors have considered distributed inference approaches, where the data are divided among multiple workers (cores, machines or a combination of both). The computations are then performed in parallel and the resulting partial estimators are finally combined to approximate the intractable global estimator. In this paper, we focus on the scenario where no communication exists among the workers, deriving efficient linear fusion rules for the combination of the distributed estimators. Both a constrained optimization perspective and a Bayesian approach (based on the Bernstein-von Mises theorem and the asymptotic normality of the estimators) are provided for the derivation of the proposed linear fusion rules. We concentrate on finding the minimum mean squared error (MMSE) global estimator, but the developed framework is very general and can be used to combine any type of unbiased partial estimators (not necessarily MMSE partial estimators). Numerical results show the good performance of the algorithms developed, both in problems where analytical expressions can be obtained for the partial estimators, and in a wireless sensor network localization problem where Monte Carlo methods are used to approximate the partial estimators.