Neural networks are routinely used for nonparametric regression modeling. The interest in these models is growing with ever-increasing complexities in modern datasets. With modern technological advancements, the number of predictors frequently exceeds the sample size in many application areas. Thus, selecting important predictors from the huge pool is an extremely important task for judicious inference. This paper proposes a novel flexible class of single-layer radial basis functions (RBF) networks. The proposed architecture can estimate smooth unknown regression functions and also perform variable selection. We primarily focus on Gaussian RBF-net due to its attractive properties. The extensions to other choices of RBF are fairly straightforward. The proposed architecture is also shown to be effective in identifying relevant predictors in a low-dimensional setting using the posterior samples without imposing any sparse estimation scheme. We develop an efficient Markov chain Monte Carlo algorithm to generate posterior samples of the parameters. We illustrate the proposed method's empirical efficacy through simulation experiments, both in high and low dimensional regression problems. The posterior contraction rate is established with respect to empirical distance assuming that the error variance is unknown, and the true function belongs to a Hölder ball. We illustrate our method in a Human Connectome Project dataset to predict vocabulary comprehension and to identify important edges of the structural connectome.

中文翻译：

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用于平滑函数估计和变量选择的多元高斯 RBF 网络

神经网络通常用于非参数回归建模。随着现代数据集日益复杂，人们对这些模型的兴趣也在增长。随着现代技术的进步，预测变量的数量经常超过许多应用领域的样本量。因此，从庞大的池中选择重要的预测变量是明智推理的一项极其重要的任务。本文提出了一种新型灵活的单层径向基函数 (RBF) 网络。所提出的架构可以估计平滑的未知回归函数并执行变量选择。由于其吸引人的特性，我们主要关注高斯 RBF 网络。对 RBF 其他选择的扩展相当简单。所提出的架构还被证明可以有效地使用后验样本识别低维设置中的相关预测因子，而无需强加任何稀疏估计方案。我们开发了一种高效的马尔可夫链蒙特卡罗算法来生成参数的后验样本。我们通过模拟实验说明了所提出的方法在高维和低维回归问题中的经验有效性。后收缩率是根据经验建立的 在高维和低维回归问题中。后收缩率是根据经验建立的 在高维和低维回归问题中。后收缩率是根据经验建立的距离假设误差方差未知，并且真实函数属于 Hölder 球。我们在人类连接组项目数据集中说明了我们的方法来预测词汇理解并识别结构连接组的重要边缘。