论文标题
专家模型的高维混合物的预测集
Prediction Sets for High-Dimensional Mixture of Experts Models
论文作者
论文摘要
大型数据集使构建可以捕获响应变量和功能之间异质关系的预测模型成为可能。高维线性专家模型的混合物认为，观测值来自高维线性回归模型的混合物，其中混合物的权重本身是依赖性的。在本文中，我们展示了如何在高维设置中为$ \ ell_1 $ penalizatization构建的有效预测集。我们利用一种偏见程序来说明刑罚引起的偏见，并提出了一种新的策略，以组合间隔以形成一个预测设置，并在混合设置中保证了覆盖范围。合成示例和对超导材料临界温度的预测的应用表明，我们的方法具有可靠的实践性能。
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.
