We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as scalable approximations of classical Gaussian processes. Variable selection is achieved by conditioning the process mean and covariance function on a random set that represents the indices of contributing variables. A priori beliefs regarding this set control the variable selection, while reference priors are assigned to the remaining model parameters, ensuring numerical robustness in the process covariance matrix. We propose a Metropolis-Within-Gibbs algorithm for model inference. Evaluation using simulated data, a computer experiment approximation, and two real-world data sets demonstrate the effectiveness of our approach.

翻译：我们提出了一种新颖的贝叶斯变量选择方法，该方法采用高斯过程回归，对于提升模型可解释性与正则化效果至关重要。我们的方法运用最近邻高斯过程作为经典高斯过程的可扩展近似。变量选择通过将过程均值与协方差函数条件化于一个表示贡献变量索引的随机集合来实现。关于该集合的先验信念控制着变量选择过程，同时为其余模型参数指定参考先验，从而确保过程协方差矩阵的数值稳健性。我们提出了一种Metropolis-Within-Gibbs算法用于模型推断。通过模拟数据、计算机实验近似以及两个真实数据集的评估，验证了所提方法的有效性。