论文标题
基于内核的共识汇总
A Kernel-based Consensual Aggregation for Regression
论文作者
论文摘要
在本文中，我们介绍了一种基于内核的共识聚合方法，以解决回归问题。我们的目标是使用加权平均值灵活地组合单个回归估计器$ r_1，r_2，\ ldots，r_m $，其中权重根据某些内核功能定义，以构建目标预测。这项工作扩展了Biau等人的背景。 （2016年）到一个基于内核的框架。我们表明，这种更通用的配置也继承了基本一致估计器的一致性。此外，提出了一种基于梯度下降算法的优化方法，以有效，快速估计策略的关键参数。还提供了在几个模拟和实际数据集上进行的数值实验，以说明梯度下降算法在估计关键参数和改善方法的整体性能时，通过引入更平滑的核函数来提高梯度下降算法。
In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined based on some kernel function to build a target prediction. This work extends the context of Biau et al. (2016) to a more general kernel-based framework. We show that this more general configuration also inherits the consistency of the basic consistent estimators. Moreover, an optimization method based on gradient descent algorithm is proposed to efficiently and rapidly estimate the key parameter of the strategy. The numerical experiments carried out on several simulated and real datasets are also provided to illustrate the speed-up of gradient descent algorithm in estimating the key parameter and the improvement of overall performance of the method with the introduction of smoother kernel functions.
