Large datasets make it possible to build predictive models that can capture heterogenous relationships between the response variable and features. The mixture of high-dimensional linear experts model posits that observations come from a mixture of high-dimensional linear regression models, where the mixture weights are themselves feature-dependent. In this paper, we show how to construct valid prediction sets for an $\ell_1$-penalized mixture of experts model in the high-dimensional setting. We make use of a debiasing procedure to account for the bias induced by the penalization and propose a novel strategy for combining intervals to form a prediction set with coverage guarantees in the mixture setting. Synthetic examples and an application to the prediction of critical temperatures of superconducting materials show our method to have reliable practical performance.
翻译:大型数据集使得有可能建立能够捕捉反应变量和特征之间异种关系的预测模型。高维线性专家模型的组合假设,观测来自高维线性回归模型的混合体,混合物的重量本身取决于特征。在本文中,我们展示了如何为高维环境中的1美元1美元经惩罚的专家混合模型构建有效的预测组。我们使用偏差程序来说明惩罚引起的偏差,并提出了一个新颖的战略,将间隔合并成一个预测组,在混合物设置中保证覆盖。合成实例和超导材料临界温度预测的应用显示了我们可靠实际性能的方法。