Direct and approximately valid probabilistic inference on a class of statistical functionals
Direct and approximately valid probabilistic inference on a class of statistical functionals
复制标题
DOI：
10.1016/j.ijar.2022.09.011
复制
发表时间：
2021-12
期刊：
影响因子：
--
通讯作者：
Leonardo Cella;Ryan Martin
中科院分区：
文献类型：
--
作者：
Leonardo Cella;Ryan Martin
现有的概率推理框架假设感兴趣的数量是假设的统计模型的参数。然而，在机器学习应用中，通常没有统计模型/参数；兴趣的数量是一个统计函数，是潜在分布的一个特征。基于模型的方法只能间接地处理这类问题，通过将模型参数边缘化到感兴趣的实际数量。在这里，我们开发了一个广义推理模型（IM）框架，用于对兴趣数量的直接概率不确定性量化。特别地，我们构建了一个数据依赖的、基于自举的可能性度量，用于不确定性的量化和推理。然后，我们证明了这种新方法提供了近似有效的推理，在某种意义上，分配给关于未知的假设的似然值在频率论意义上是渐近校准的。除其他事项外，这意味着从我们提出的IM导出的基础函数的置信区域是近似有效的。该方法在包括分位数回归在内的关键示例和个性化医疗应用中表现良好。
Existing frameworks for probabilistic inference assume the quantity of interest is the parameter of a posited statistical model. In machine learning applications, however, often there is no statistical model/parameter; the quantity of interest is a statistical functional, a feature of the underlying distribution. Model-based methods can only handle such problems indirectly, via marginalization from a model parameter to the real quantity of interest. Here we develop a generalized inferential model (IM) framework for direct probabilistic uncertainty quantification on the quantity of interest. In particular, we construct a data-dependent, bootstrap-based possibility measure for uncertainty quantification and inference. We then prove that this new approach provides approximately valid inference in the sense that the plausibility values assigned to hypotheses about the unknowns are asymptotically well-calibrated in a frequentist sense. Among other things, this implies that confidence regions for the underlying functional derived from our proposed IM are approximately valid. The method is shown to perform well in key examples, including quantile regression, and in a personalized medicine application.