Valid inferential models for prediction in supervised learning problems
Valid inferential models for prediction in supervised learning problems
复制标题
用于预测监督学习问题的有效推理模型
DOI：
10.1016/j.ijar.2022.08.001
复制
发表时间：
2022
影响因子：
3.9
通讯作者：
Martin, Ryan
中科院分区：
文献类型：
--
作者：
Cella, Leonardo;Martin, Ryan
预测是统计学中的一个基本问题，其中观察到的数据用于量化未来观察的不确定性。具有覆盖概率保证的预测集是一种常见的解决方案，但从为未来可观察的相关断言分配信念的意义上来说，这些并不能提供概率不确定性量化。或者，我们建议使用概率预测器，即给定观测数据的待预测观测值的完全指定（不精确）的概率分布。概率预测器在某种意义上是可靠或有效的，这一点至关重要，在这里我们提供有效性的概念并探讨其含义。我们还提供了一个通用的推理模型构造，可以产生一个可证明有效的概率预测器，并带有回归和分类的说明。
Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide probabilistic uncertainty quantification in the sense of assigning beliefs to relevant assertions about the future observable. Alternatively, we recommend the use of a probabilistic predictor, a fully-specified (imprecise) probability distribution for the to-be-predicted observation given the observed data. It is essential that the probabilistic predictor is reliable or valid in some sense, and here we offer a notion of validity and explore its implications. We also provide a general inferential model construction that yields a provably valid probabilistic predictor, with illustrations in regression and classification.