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.
翻译:假设的统计模型的参数是假设的统计模型参数;然而,在机器学习应用中,往往没有统计模型/参数;利息的数量是统计功能,基本分布的一个特征;基于模型的方法只能通过从模型参数边缘化到实际利益数量间接处理这类问题;我们在此开发了一个通用的推断模型框架,用于直接预测不确定性量化利息数量;特别是,我们为不确定性的量化和推断,构建了一个依赖数据、基于靴子的陷阱可能性计量。然后,我们证明这一新方法提供了大致有效的推论,因为为未知物设定的假设物的概率值在经常意义上是同样具有说服力的。这除其他外,意味着对从我们提议的IM中得出的基本功能的信任区域大致有效。这种方法在关键例子中表现良好,包括量化回归,以及个人化医学应用。