Distributed Quantile Regression Over Sensor Networks

As one of the essential statistical tools, quantile regression has been applied to a variety of application areas. Compared with mean regression, which depicts only the relationship between the mean of a response variable and its covariates, quantile regression is able to provide a more complete description of the relationships between the response variable and its covariates by estimating a series of quantiles instead of the mean only. In addition, quantile regression is robust to outliers and does not require any distributional assumption. In many practical applications, the data used for quantile regression can be collected by wireless sensor networks. However, to the best of our knowledge, the existing methods for quantile regression are all developed in the centralized framework, which are not preferred in wireless sensor networks due to heavy computation and communication burdens and some privacy issues. In this paper, we propose a distributed quantile regression algorithm. In the proposed algorithm, each node estimates the global parameter vector of a linear regression model over a wireless sensor network through both the computation based on its local data and the cooperation with its neighbors. Considering that numerous natural and artificial systems and signals are sparse, we also propose a
$l_1$
-distributed quantile regression (
$l_1$
-dQR) algorithm, which exploits the sparsity, to improve the performance of the method in quantile regression based on sparse models. The convergence analyses of the proposed algorithms are studied, and simulations are also conducted to verify the effectiveness of the proposed algorithms.