On the Feasibility of Distributed Kernel Regression for Big Data

Abstract In modern scientific research, massive datasets with huge numbers of observations are frequently encountered. To facilitate the computational process, a divide-and-conquer scheme is often used for the analysis of big data. In such a strategy, a full dataset is first split into several manageable segments; the final output is then averaged from the individual outputs of the segments. Despite its popularity in practice, it remains largely unknown that whether such a distributive strategy provides valid theoretical inferences to the original data. In this paper, we address this fundamental issue for the distributed kernel regression (DKR), where the algorithmic feasibility is measured by the generalization performance of the resulting estimator. To justify DKR, a uniform convergence rate is needed for bounding the generalization error over the individual outputs, which brings new and challenging issues in the big data setup. Under mild conditions, we show that, with a proper number of segments, DKR leads to an estimator that is generalization consistent to the unknown regression function. The obtained results justify the method of DKR and shed light on the feasibility of using other distributed algorithms for processing big data. The promising preference of the method is supported by both simulation and real data examples

Shifting Death to their Alternatives: The Case of Toll Motorways.

A renewed interest on the use of tolls for funding motorways and regulating their demands has been recovered in the last years. However, less attention has been put to the road safety effects derived from this policy. Although toll motorways show quality levels equal or above free motorways, charging users for the use of better infrastructure shifts some traffic to their low quality adjacent alternatives. In the present study we test whether charging for the use of the better road might negatively affect road safety in the worst adjacent road. The results confirm our hypothesis opening a new concern.Road Safety, Tolls, Motorways and Transportation