Nonparametric predictive distributions based on conformal prediction
Nonparametric predictive distributions based on conformal prediction
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DOI：
10.1007/s10994-018-5755-8
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发表时间：
2019-03-01
期刊：
影响因子：
7.5
通讯作者：
Xie, Min-ge
中科院分区：
文献类型：
--
作者：
Vovk, Vladimir;Shen, Jieli;Xie, Min-ge
本文应用保角预测来推导出在非参数假设下有效的预测分布。也就是说，我们引入和探索预测分布函数，总是满足一个自然属性的有效性方面的保证覆盖IID观察。重点是我们称之为最小二乘预测机（LSPM）的预测算法。LSPM将经典的Dempster-Hill预测分布推广到非参数回归问题。如果最小二乘线性回归的标准参数假设成立，则LSPM在自然意义上与Dempster-Hill过程一样有效。如果这些参数假设失败，LSPM仍然有效，只要观测是IID。
This paper applies conformal prediction to derive predictive distributions that are valid under a nonparametric assumption. Namely, we introduce and explore predictive distribution functions that always satisfy a natural property of validity in terms of guaranteed coverage for IID observations. The focus is on a prediction algorithm that we call the Least Squares Prediction Machine (LSPM). The LSPM generalizes the classical Dempster-Hill predictive distributions to nonparametric regression problems. If the standard parametric assumptions for Least Squares linear regression hold, the LSPM is as efficient as the Dempster-Hill procedure, in a natural sense. And if those parametric assumptions fail, the LSPM is still valid, provided the observations are IID.