论文标题
贝叶斯投影追求回归
Bayesian Projection Pursuit Regression
论文作者
论文摘要
在投影追踪回归（PPR）中，m“脊函数”的总和是一个未知的响应函数，这是多变量输入空间的一维投影的灵活函数。传统上，优化例程用于通过顺序算法估算投影方向和脊函数，通常通过交叉验证选择m。我们介绍了第一个贝叶斯版本的PPR，它具有准确的不确定性量化的好处。为了了解投影方向和脊功能，我们应用了用于单个脊功能案例的方法（M = 1），称为单个索引模型，该模型确实存在贝叶斯实现；然后使用可逆的跳跃MCMC了解脊功能的数量。我们在20个模拟方案和23个真实数据集中评估了模型的预测能力，并在针对一系列最新的回归方法的烘烤中评估了模型。它的有效性能表明，贝叶斯投影追求回归是现有回归工具箱的宝贵补充。
In projection pursuit regression (PPR), an unknown response function is approximated by the sum of M "ridge functions," which are flexible functions of one-dimensional projections of a multivariate input space. Traditionally, optimization routines are used to estimate the projection directions and ridge functions via a sequential algorithm, and M is typically chosen via cross-validation. We introduce the first Bayesian version of PPR, which has the benefit of accurate uncertainty quantification. To learn the projection directions and ridge functions, we apply novel adaptations of methods used for the single ridge function case (M=1), called the Single Index Model, for which Bayesian implementations do exist; then use reversible jump MCMC to learn the number of ridge functions M. We evaluate the predictive ability of our model in 20 simulation scenarios and for 23 real datasets, in a bake-off against an array of state-of-the-art regression methods. Its effective performance indicates that Bayesian Projection Pursuit Regression is a valuable addition to the existing regression toolbox.
